# Constant of Integration

The reverse operation of finding a derivative is called the antiderivative. A function $F$ is an antiderivative of a function $f$ if $F ’(x)$ = $f (x)$. That antiderivative is nothing but the differentiation. Integration is the process of evaluating an indefinite integral or a definite integral.

$\int_a^b$ $f(x)dx$

$\int_a^b$ $f(x)dx$

The definite integral is a number whose value depends on the function $f$ and the numbers $a$ and $b$, and it is defined as the limit of a Riemann sum.

$f(x)$ = $\int$ $f'(x)dx$

$D_x\ [f(x)]$ = $f'(x)$

The indefinite integral $\int$ $f’(x)dx$ is defined as a function $g$ such that its derivative $Dx[f(x)]$ = $f’(x)$. Indefinite integral involves an arbitrary constant, for example let us find the integral of $x^2$.

$\int$ $x^2 dx$ = $x^3 + c$

$\int$ $x^2 dx$ = $x^3 + c$

The arbitrary constant $c$ is called a constant of integration.