How to write in symbols the sum defining the indefinite integral of function f, in case one has no explicit formula for f?

Question

• If I am told that $f(x) = x$, I can write that :

the indefinite integral of $f$ is $\frac{x^2}{2} + C.$

• There might be cases in which it would be convenient to say the same thing for some function $f$, without having any explicit formula for $f$. In such cases, how could the sum be written? Is there a symbol to denote the first term of the sum?

What I would like is to be able to complete this general statement for an unspecified function f

" indefinite integral of $f =$ ______ $(x) +C $".

Answer 1

If the function $f$ is continuous you can write something as $$ \int_a^x f(t)dt +C $$

Answer 2

One possibility is to say

If $F(x)$ is a function such that $F'(x)=f(x)$, then $$\int f(x)\,dx=F(x)+c.$$