Judge PARKER dissents in a separate opinion.
STRAUB, Circuit Judge:Defendant and Appellant the Terminix International Company L.P. (“Terminix”) appeals from an order of the United States District Court for the District of Connecticut (Avin W. Thompson, Judge), denying its motion to dismiss or in the alternative to stay the litigation and compel arbitration, pursuant to the Federal Arbitration Act (“FAA”), 9 U.S.C. § 1 et seq., in light of an arbitration clause contained in a written agreement between the parties for termite control services. See Mehler v. Terminix Int’l Co., No. 397CV2390, 1998 WL 893149 (D.Conn. Sept.28, 1998). We conclude that the agreement containing the indisputably broad arbitration clause encompassed the entire contractual relationship between the parties and that, in any event, the claims relate to the agreement, irrespective of the agreement’s temporal or substantive breadth. Therefore, we reverse the order of the District Court denying Terminix’s motion and remand with instructions to stay the proceedings and direct the parties to proceed to arbitration.
BACKGROUND
This dispute arises out of an accident that occurred while Terminix was providing termite extermination services at the home of Jeffrey N. Mehler and Mary S. Russell. Terminix performed the first of a two-day extermination treatment of the plaintiffs’ home on July 19, 1996, and returned to complete the treatment on July 24, 1996. The plaintiffs contend, and Ter-minix does not dispute, that in the course of performing these services, the Terminix technician punctured their underground home heating oil line, resulting in the dis*46charge of oil to the plaintiffs’ and their neighbors’ property.
Also on July 19, the Terminix representative provided the plaintiffs with a document (“Agreement”), with the heading “Termite Protection Plan” on the first page, which was signed by Mehler on that date. The Agreement provides: “Effective UPON COMPLETION through 2 YEARS, for the sum of $1500.00 + TAX, Terminix will provide the necessary service to protect the identified property against the attack of subterranean termites .... ” (The words in all caps were filled in by hand by the Terminix representative). The Agreement'further contains a note to the customer in the upper right-hand corner stating that: “This is a service order and copy of the Termite Protection Plan. This service order is contingent on approval of the Terminix branch manager. You will receive written confirmation that your contract is in effect when the work is completed and Terminix has been paid in full.” Further, the Agreement specifies that “[t]his plan provides protection against new subterranean termite damage to the structure and contents. If new damage occurs during the contract term, Terminix will ... arrange for the necessary repairs or replacement.... ”
“New damage” is defined in the Protection Plan as “damage done by subterranean termites subsequent to the inception date of this contract; the definition excludes damage existing at the inception date.” “[0]ld damage ... is not covered under this Plan.” Paragraph 8 of the Terms and Conditions states: “ENTIRE AGREEMENT. The Service Order signed at the time of purchase, the Termite Protection Plan and- the Inspection Graph constitute the entire agreement between the parties and no other representations or statements will be binding upon the parties.” Paragraph 9 of the Terms and Conditions contains an arbitration provision, which states in relevant part: “The Purchaser and Terminix agree that any controversy or claim between them arising out of or relating to this agreement shall be settled exclusively by arbitration.”
The Protection Plan attaches, and expressly incorporates, two graphs dated July 12, 1996, and signed by Mehler on July 19, 1996, one showing the plaintiffs’ stand-alone garage and one showing their residence and reflecting the pre-existence or non-existence of termite activity and damage on that date. According to Termi-nix, the numbers on the graph, ie. “117,” reflect specifications for initial treatment of the property. Lastly, the Agreement states that “Terminix has provided the Purchaser with a copy of the manufacturer’s specimen label ..". for the termiti-cide(s) which will be used to treat the above-named property.”
At some point after the initial two-day treatment was completed, Terminix sent the plaintiffs a document entitled “Termite Guarantee,” which references and restates in part the Protection Plan in the Agreement, and states that the Protection Plan “provides for arbitration of any controversy or claim arising out of or [relating] to the Plan.” Also at some point after the completion of the two-day July termite service, Terminix provided, and Russell signed, a “Completion Certificate,” stating that the work at her home had been performed “according to specifications submitted to [her] by Terminix.” Finally, the plaintiffs do not dispute that only one $1500 fee, as specified in the Agreement, was paid to Terminix for all work done by Terminix, including that on July 19 and July 24.
On October 30, 1997, Terminix initiated arbitration proceedings to resolve the plaintiffs’ claim that Terminix is liable for the discharge of oil to their and their neighbors’ property, and the plaintiffs filed an Answering Statement with the American Arbitration Association (“AAA”) asserting that the AAA lacks jurisdiction to hear their claims because they never agreed to arbitrate the dispute placed before the AAA.
*47On November 12, 1997, the plaintiffs filed a complaint in the District of Connecticut seeking, inter alia, compensation for property damage and personal injury under various tort theories; punitive damages under the Connecticut Unfair Trade Practices Act (“CUTPA”), Conn. Gen.Stat. § 42-110a et seq.; invalidation of the contract between the parties as unfair, oppressive and unconscionable; and declaratory relief that the claims at issue do not fall within the arbitration clause contained in the Agreement between the parties. Terminix filed a motion to dismiss or in the alternative to stay the litigation pending arbitration, pursuant to the FAA in the District Court, which was denied on September 28,1998.
This timely appeal followed.
DISCUSSION
I. Applicability of the FAA and Standard of Review
The FAA creates a “body of federal substantive law of arbitrability, applicable to any arbitration agreement within the coverage of the [FAA].” Moses H. Cone Mem. Hosp. v. Mercury Constr. Corp., 460 U.S. 1, 24, 103 S.Ct. 927, 74 L.Ed.2d 765 (1983). There is no dispute on appeal that the FAA applies to the arbitration agreement at issue, which affects interstate commerce. See id.; 9 U.S.C. §§ 1 & 2. Section 3 of the FAA provides for stays of federal proceedings pending arbitration under appropriate circumstances. See generally 9 U.S.C. § 3.
A court asked to stay proceedings pending arbitration must resolve two issues relevant here: “first, it must determine whether the parties agreed to arbitrate; second, it must determine the scope of that agreement.” Oldroyd v. Elmira Sav. Bank, 134 F.3d 72, 75 (2d Cir.1998). The plaintiffs assert that the District Court concluded that the first element was not satisfied in this case. Clearly, this assertion is incorrect. While stating the general principle that “parties may not be compelled to submit a dispute to arbitration unless they have agreed to do so,” the court framed the issue before it as the “scope of the parties’ arbitration agreement.” Thus, the District Court correctly concluded that there was an arbitration clause to which the parties had agreed, and the relevant question, addressed by the District Court and on review, is whether the claims are within the scope of that clause, either because the claims arise under the contract containing the broad arbitration clause, or because they relate to the contract containing the clause. We review a district court’s determinations on these issues de novo. See id. at 76.
II. The Scope of the Agreement
A. The Agreement Between the Parties Is a Unified Contract
The District Court rested its decision on a finding that, although there was a broad agreement to arbitrate between the parties, the plaintiffs’ claims were not within the scope of that agreement. The District Court’s main concern was that the arbitration clause was contained within a contract that, in the court’s view, did not pertain to the services at issue. See Mehler v. Terminix, 397CV2390, 1998 WL 893149, at *5 (D.Conn. Sept. 28, 1998) (stating that “work that must be completed before a contract can become effective cannot be within the scope of that contract, unless there is some express provision specifying how that is to be so”).
We take no issue with the District Court’s decision to determine the relationship between the claims and the scope of the contract containing the arbitration clause. See Collins & Aikman Prods. Co. v. Building Sys., Inc., 58 F.3d 16, 23 (2d Cir.1995) (“the task of determining whether a claim or a set of claims ‘arises out of or relates to’ the particular contract in which the arbitration clause is found” is a task properly done by the district court); Prudential Lines, Inc. v. Exxon Corp., 704 F.2d 59, 63 (2d Cir.1983) (“The question of *48whether a dispute between the parties is covered by the arbitration agreement is for the courts to decide.”). But, we disagree with the court’s resolution of that issue.
The plaintiffs argue, and the District Court seems to have accepted, that there were two separate contracts: an oral one entered into between the parties before services were rendered on July 19, which pertained to the initial termite treatment on July 19 and July 24, and the written one, containing the arbitration clause, pertaining only to future termite protection services and effective after the date that the oil puncture occurred. Thus, the plaintiffs argue, because their claim arose under a distinct, earlier contract from the one containing an arbitration clause, the clause — no matter how broadly worded— cannot relate back to the claims under a separate contract.
Terminix, by contrast, argues that there was only one contract between the parties, the written Agreement which contains three parts: (1) application of termiticide to the property, by reference to the service order and graphs attached to the Agreement; (2) the Protection Plan, which provides for future services; and (3) the guarantee of those future services. We agree with Terminix.
As the District Court correctly stated, in deciding whether the parties agreed to arbitrate a certain matter, courts should generally apply state-law principles that govern the formation of contracts. See First Options of Chicago, Inc. v. Kaplan, 514 U.S. 938, 944, 115 S.Ct. 1920, 131 L.Ed.2d 985 (1995). The District Court cited Connecticut’s policy that “in the absence of an express term in the ... agreement itself, ... agreements do not typically apply retroactively,” Housing Auth. of Norwalk v. Ross, No. SPNO 9206-A2880, 1993 WL 394294, at *4 (Conn.Super.Ct. July 19, 1993), and concluded that the Agreement, and accordingly the arbitration clause, could not apply retroactively given this rule of construction. See Mehler, 1998 WL 893149, at *8. The flaw in this conclusion, however, is that it assumes that the Agreement covers only the period after the initial two-day services had been rendered — when the accident occurred — and, therefore, would have to apply retroactively to cover the instant dispute.
Our reading of the Agreement leads us to conclude that it constitutes a unified contract for extermination and continual protection, encompassing all aspects of the services, beginning on July 19, provided by Terminix to the plaintiffs. First, the Agreement was signed on the day, and before, the initial service began. Second, the Agreement expressly refers to itself as containing two separate parts, namely, the “Service Order” and the “Termite Protection Plan.” Third, the Agreement attaches and expressly incorporates graphs specifying the termite damage at that time and the treatment to be provided during the initial two days. Fourth, the Agreement states that the Protection Plan, the Service Order signed at the time of purchase, and the Inspection Graphs constitute the entire agreement between the parties. Fifth, the plaintiffs signed a statement that work had been done on their house according to specifications submitted by Terminix, and those specifications were contained in the graphs incorporated into the Agreement. Sixth, the plaintiffs’ own complaint supports the conclusion that there was only one contract. See Oldroyd, 134 F.3d at 77 (“In determining whether a particular claim falls within the scope of the parties’ arbitration agreement, we focus on the factual allegations in the complaint rather than the legal causes of action asserted.”). The plaintiffs’ complaint repeatedly alleges that Terminix punctured their fuel oil line, “[w]hile performing work under the contract,” or “in connection with the termite control contract,” or during “the work planned under the contract.” Finally, that the plaintiffs made only one payment to Terminix for all work done by Terminix supports the notion that there was only *49one contract between the parties. See Crowther v. Gerber Garment Tech., Inc., 8 Conn.App. 254, 263, 513 A.2d 144, 149 (Conn.App.Ct.1986) (“The conduct of the parties regarding the terms of a contract is a useful and proper aid to its interpretation.”).
The Agreement, and the Termite Guarantee that refers to and incorporates the Termite Protection Plan, do provide for an effective starting date after the date of the initial services. However, a reasonable reading of the Agreement, in light of its language, the timing of its execution, and the conduct of the parties, indicates that that date pertains only to the Protection Plan and the Guarantee, which constitute only part of the Agreement as a whole. See Venture Partners, Ltd. v. Synapse Techs. Inc., 42 Conn.App. 109, 118, 679 A.2d 372, 377 (Conn.App.Ct.1996) (stating that the determinative test in deciding whether a contract constitutes a unified whole “is in ascertaining from the language used, read in the light of the surrounding circumstances, what was the intention of the parties”); Ginett v. Computer Task Group, Inc., 962 F.2d 1085, 1098-99 (2d Cir.1992) (concluding based on various factors that it would be an unreasonable reading of the contract not to read it as a “unified, inseparable whole”). As Terminix explains, a customer has the option to purchase a comprehensive plan against termite infestation on their property, including the initial extermination and the future guarantee, as the plaintiffs did. The future guarantee, as common sense dictates and the Agreement reflects, does not become effective until after the initial two-day treatment by Terminix has been completed and the customer pays the $1500 fee. Read in this light, the Agreement is distinguishable from the contracts at issue in the cases relied upon by the plaintiffs.
In Scinto v. Sosin, 51 Conn.App. 222, 721 A.2d 552 (Conn.App.Ct.1998), cert. denied, 247 Conn. 963, 724 A.2d 1125 (1999), for example, the trial court limited the scope of an arbitration clause to those issues arising from construction occurring after November 15, 1990, where the contract containing the clause was memorialized and executed on that date. The appellate court affirmed that decision on the ground that the construction contract specifically limits performance to work performed after the execution date of the contract. See id. at 240, 721 A.2d at 562. Our reading of the Agreement here, by contrast, leads us to conclude that it encompasses all of the work done by Termi-nix, including that done during the two-day period when the instant dispute arose.
B. The Unified Contract Contains an Indisputably Broad Arbitration Clause
Having concluded that the claims at-issue arise under the contract containing the arbitration clause, we must determine whether the arbitration clause in the Agreement covers those claims. Once the court has determined the threshold issue of whether an arbitration agreement exists, and that the agreement is a broad one, as here, the court must compel arbitration “unless it may be said with positive assurance that the arbitration clause is not susceptible of an interpretation that covers the asserted dispute.” Collins, 58 F.3d at 19 (internal quotation marks and citation omitted); see also First Options of Chicago, 514 U.S. at 945, 115 S.Ct. 1920 (noting that “issues will be deemed arbitrable unless it is clear that the arbitration clause has not included them” (internal quotation marks omitted)).
There is no dispute that the arbitration clause at issue is a classically broad one. See Oldroyd, 134 F.3d at 76. The clause provides for arbitration of “any controversy or -claim between [the parties] arising out of or relating to” the Agreement. We have previously decided that this is “precisely the kind of broad arbitration clause that justifies a presumption of arbitrability.” Id. Accordingly, because an indisputably broad arbitration clause is contained *50in the Agreement that encompasses the claims at issue, the motion to stay proceedings pending arbitration should have been granted.
III. The Relationship of the Claims to the Agreement
Terminix further contends that, contrary to the District Court’s assumption, the issue sought to be arbitrated need not constitute a breach of the contract containing the arbitration clause. Rather, the relevant question is whether the dispute “arises out of” or “relates to ” that contract. We agree with Terminix in this respect as well.
In Collins, for example, there were indisputably two separate but related contracts at issue giving rise to the plaintiffs’ claims: a 1977 contract containing an arbitration clause, and a 1988 agreement, which did not. See 58 F.3d at 21. With respect to the claims that were articulated as breaches of the 1988 agreement .only, we stated that “[t]he question is not whether the ... claims arise under the 1988 Agreement, which has no arbitration clause; the question is whether these claims plead conduct that ‘aris[es] out of or [is] related to’ the 1977 Contracts, which do[ ] have such a clause.” Id.
The precise phrasing of this standard has varied. See, e.g., id. (stating that “[i]f the allegations underlying the claims ‘touch matters’ covered by the parties’ [contracts], then those claims must be arbitrated”); Coudert v. Paine Webber Jackson & Curtis, 705 F.2d 78, 82 (2d Cir.1983) (deciding whether claims “pertain to” the contract at issue); Popper v. Monroe, 673 F.Supp. 1228, 1230 (S.D.N.Y.1987) (determining whether claims are “integrally linked” to the contractual relation). But see Leadertex, Inc. v. Morganton Dyeing & Finishing Corp., 67 F.3d 20, 29 (2d Cir.1995) (stating that all of the above tests are not particularly helpful and that the key inquiry is what was the reasonable expectation of the parties who commit themselves to be bound by the provisions of the arbitration agreement). Nonetheless, it is clear that we have not limited arbitration claims to those that constitute a breach of the terms of the contract at issue. See, e.g., Oldroyd, 134 F.3d at 77 (concluding that claims were within the scope of an arbitration clause because the claims “touched upon matters covered by the ... agreement” containing the clause).
There is no question that the plaintiffs’ claims relate to the Agreement, which, by its terms, provides for arbitration of claims that are only related to it. The Agreement, by express incorporation of the graphs and explicit reference to the treatment that “will be” used, provides the specifications for the initial two-day treatment during which the oil puncture occurred. Thus, irrespective of our construction of the Agreement as a unified whole, given the presumption of arbitrability that applies to broad arbitration clauses, see id. at 76-77 (reversing a district court’s determination that a retaliatory discharge claim was not within the scope of a broad arbitration clause, based in part on the presumption of arbitrability), the motion to stay the litigation pending arbitration should have be granted on this basis as well.
CONCLUSION
We have reviewed all of the plaintiffs’ remaining arguments on appeal and find them to be without merit. For the foregoing reasons, we reverse the order of the District Court denying Terminix’s motion and remand with instructions to stay the proceedings and direct the parties to proceed to arbitration.