Integration is the reversal process that recovers a function from its derivative (or rate of change).
By doing integration it is possible to evaluate displacement over a time period if the velocity function is given.
Initially the reversal approach of integration provides formulas for finding the antiderivatives of common functions. In its advanced approach, integration is viewed as the limit of a sum and used to determine the volumes and areas and is also widely applied in Physics.
Let us look at the definition of integrals, the formulas and rules for integration and its application.

Integral is defined using antiderivatives.

Antiderivative Definition

A function F is an antiderivative of f over an interval, if F'(x) = f(x) for all values of x in the interval.

As adding constants to F(x) does not alter the derivative, F(x) + c is the most general antiderivative of f(x)
and it is commonly known as its integral.

Suppose F(x) is an antiderivative of f(x). The indefinite integral of f(x) with respect to x is defined as
$\int f(x)dx$ = F(x) + c,
where c is a constant known as constant of integration.

f(x) is called the integrand, dx defines the variable of integration as x and the process of computing the integral is known as integration.
We know $\frac{d}{dx}sinx$ = cos x.

Thus sin x is the antiderivative of F(x). The integral of cos x is hence $\int cosx dx$ = sin x + c
where c is the constant of integration.