Integral calculus is a part of the field of calculus involving the concept of accumulation. The process of finding integrals (numerically or exactly) is a fundamental tool. It is often associated with differential calculus, as differentiation and integration have been proven to be inverse processes.
In high school or college calculus courses, it is typically introduced with a discussion of antiderivatives near the end of the first semester and then studied extensively throughout the second semester; if there is a third semester, it typically covers integration in higher dimensions (e.g., double integrals and so forth).
Integration in its simplest of terms is the process of finding the product between the dependent (y) and the independent axis (x) between two points (a,b) on the independent axes, which is basically the area under the dependent axis (y) that is above the independent axis (x).