Antiderivative

A function $F$ whose derivative is the given function $f$ — reversing differentiation.

An antiderivative of $f$ is any function $F$ with $F'(x)=f(x)$ on the interval in question. Antiderivatives are never unique: if $F$ is one antiderivative of $f$ , so is $F(x)+C$ for any constant $C$ , since constants vanish under differentiation. Finding "the" antiderivative always means finding one representative and appending $+C$ to capture the whole family.

Examples

$F(x)=x^3$ is an antiderivative of $f(x)=3x^2$ , and so is $x^3+7$ or $x^3-100$ .
$F(x)=\sin(x)$ is an antiderivative of $f(x)=\cos(x)$ .