What does Integration generally mean by its word?

Integration is a core model of advanced mathematics, particularly in the fields of calculus and mathematical analysis. Given a function f(x) of a actual variable x and an interval [a, b] of the real line, the integral is equal to the area of a region in the xy-plane bounded by graph of f, the x-axis, and the vertical lines x = a and x = b, by way of areas below the x-axis being subtracted.

The word "integral" may as well refer to the notion of antiderivative, a function F whose derivative is the given function f. In this casing it is called an indefinite integral, while the integrals discussed in this article are named definite integrals. Few authors maintain a distinction between antiderivatives and indefinite integrals.