What Is An Indefinite Integration?

Relevant wiki: Antiderivative and Indefinite Integration

Suppose $F(x)$ is an antiderivative of $f(x)$ . That is, $F'(x) = f(x)$ . Observe that $F(x) + C$ is also a antiderivative of $f(x)$ for any value of $C$

The indefinite integral $\int f(x) \, dx$ is the set of all antiderivatives of the function $f(x)$ . This set consists of all functions of the form $F(x) + C$ , generated by taking different values of $C$ .

We can write the set in set-builder notation as:

$\int f(x) \, dx = \{ \, F(x) + C \mid C \in \mathbb{R} \, \}$

Thus we can say that the indefinite integral is a set of functions, that differ by a constant. $_\square$

also there function f: r>>>>r and the integral =complex function +c thats easy question but make u ask about area blow function