9
$\begingroup$

I understand that when we are doing indefinite integrals on the real line, we have $\int f(x) dx = g(x) + C$, where $C$ is some constant of integration.

If I do an integral from $\int f(x) dx$ on $[0,x]$, then is this considered a definite integral? Can I just leave out the constant of integration now? I am skeptical of the fact that this is a definite integral, because our value $x$ is still a variable.

3 Answers 3