In contract law, partial integration occurs when a contract contains some, but not all, terms of agreement for a contract. Restatement section 210(2).
In contrast, a complete integration is a contract that contains all terms that the parties agreed to. Restatement Second of Contracts section 210(1). It is a "complete and exclusive" expression of everything the parties have agreed to.
Whether the contract is completely or partially integrated is the first step a court must undertake in applying the Parol Evidence Rule. See Restatement Second of Contracts section 210. The Parol Evidence Rule is a prior oral rule that a written contract cannot be varied, contradicted or altered by prior oral declarations.
When does a partial integration happen? Sometimes, parties will have a written agreement but as they were signing, they orally agreed to one or more additional terms which were not written into the contract. In that case, they have a mixed contract of oral and written terms. The written document will be a partial integration of everything the parties agreed to. The paper is not the whole contract, but only a representation of some of the terms.
How do you determine integration? There are multiple approaches to determining whether a written instrument (the document portion of the contract) is totally or partially integrated. First is the Williston approach, in which the assumption is that if the written instrument looks complete, then it is integrated. The Williston approach assumes that absence of any particular terms indicate that the parties did not wish to include it in the contract at all. This approach further assumes that if terms would naturally be included but were not, then the parties must have purposely left those terms out of the contract all together. According to the Williston approach, only if the written instrument looks incomplete is it partially integrated. If it is partially integrated, then you can apply the Parol Evidence Rule. For more on the Williston approach see Mitchel v. Lath (1928).
An alternate approach to determining whether a contract is partially or totally integrated is the Corbin approach. In the Corbin approach, parties' intent when drafting the contract is key. According to this approach, a court should admit all evidence (oral and written) in order to determine the intent of the parties and whether or not they meant to include additional terms that just did not make it into the written instrument. In this approach, anything that doesn't contradict the written terms is a consistent term and the court can assume that oral agreements may have happened as part of this same contract if they were consistent terms. For more on the Corbin approach (also referred to as the common law approach to contract integration) see the case Masterson v. Sine (1968).
The Uniform Commercial Code (UCC) and United Nations Convention on Contracts for the International Sale of Goods(CISG)each have their own official standards for how to determine partial versus total integration.