General rules and explication

Integration is an inverse of differentiation. Integration can be used to find areas, volumes, central points and many useful things. Integration in one of the two main operations in calculus.
A definite integral of a function can be represented as the signed area of the region bounded by its graph:

A function f of a real variable x and an interval [a, b] of the real line, definite integral:

The integral sign ∫ represents integration. The dx indicates that we are integrating over x; x is called the variable of integration. The domain D or the interval [a, b] is called the domain of integration.

or if the domain is an interval [a, b] of x;

The term integral may also refer to the notion of the antiderivative, a function F whose derivative is the given function f. In this case, it is called an indefinite integral and is written: 

General formula: