Integration is the inverse operation of differentiation. Thus, if the derivative of f(x) is F(x), the integral, or antiderivative, of F(x) equals f(x). The definite integral of a function, f(x), denoted
can be used to determine areas, volumes, and other concepts. If the bounds of integration are not specified, as in
it is referred to as an indefinite integral.
In calculus, integration is often initially taught within the context of finding the area under the curve of a function. This can be done by approximating the area under the curve by calculating the value of the function between two points on the curve, which allows us to calculate the area of a rectangle. As we continue calculating the area between more points on the curve, we can estimate the area under the curve. The smaller the width between the two points, the more accurate the estimation. This process of approximating the area under a curve by breaking it down into an infinite sum of rectangles (or other shapes) is referred to as the Riemann sum.