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integral calculus. n. 1. (Mathematics) the branch of calculus concerned with the determination of integrals and their application to the solution of differential equations, the determination of areas and volumes, etc.Compare differential calculus.. (Mathematics) the branch of calculus concerned with the determination of integrals and their application to the solution of differential equations, the determination of areas and volumes, etc. Compare differential calculus.
i.e., without upper and lower limits, also called an antiderivative. The first fundamental theorem of calculus allows definite integrals to be computed in terms of indefinite integrals. In particular, this theorem states that if is the indefinite integral for a complex function, then. (2). This result, while taught early in elementary calculus courses, is actually a very deep result connecting the purely algebraic indefinite integral and the purely analytic (or geometric) definite integral.