Indefinite integration concept

Question

What does expression of a function which is indefinitely integrated represents like if we have a function $2x$,

Integrating with respect to $x$(independent variable) we get $x^{2}$ , so what does this $x^{2}$ represents?

Answer 1

Suppose that the function to be integrated is $f(x)$, and the antiderivative exists which is $F(x)$.

We can then say that $F$ is the function whose rate of change is $f$. In symbols, \begin{gather*}\dfrac{\mathrm{d}}{\mathrm{d}x} F(x)= f(x), \\ \int f(x) \, \mathrm{d}x = F(x) + c\end{gather*}