If I want to show that $F(x)$ is antiderivative of $f(x),$ then usually I find $F'(x).$ And if $F'(x)=f(x)$, then $F$ is antiderivative, otherwise not.
My question is if I want to show that $F$ is antiderivative, can I also say that $$\int f(x)\, dx$$, and if $$\int f(x)\, dx = F(x),$$ then the answer is yes, otherwise not. Is not there a problem with a constant in this method. So for me it seems like that I cannot use it. Am I right?