Antiderivative or indefinite integral is the family of functions the derivative of which gives the original function. Now, let's elaborate the process.
Suppose $F(x)$ is the derivative of the function $f(x)$ which means that the instantaneous rate of change of $f(x)$ with respect to $x$ is $F(x)$ . $$\dfrac{d{f(x)}}{dx} = F(x)$$ Now, $$d{f(x)} = F(x)dx$$ This is the small change of $f(x)$ when there is a change of $x$ by $dx$ . Upto this point, it is correct. Then, abrubtly what books do is $$\int d{f(x)} = \int F(x)dx \implies f(x) = \int F(x)dx + C$$ . But what does this $\int$ mean? It is the counterpart of summation. So , summing $d{f(x)}$ gives the whole change in $f(x)$ but doesn't give the function $f(x)$ . So, why did the process go like that to give the function?? It is rather giving the change in function. So, why do the books do like that??? I am confused. Please help me explaining the process.