parseval for a continuos but limited signal

I have a question about the parseval relation written here https://en.wikipedia.org/wiki/Parseval%27s_theorem (In the chapter Notation used in physics).

If I have a signal continuous but limited (so it does not go from $\infty$ to $\infty$ but from 0 to T, can The Parseval theorem be applied?

Answer

Sure. You can can just integrate in the time domain from $0$ to $T$ since the area outside $[0, T]$ is 0.

Please note that you still must integrate from $-\infty$ to $+\infty$ in the frequency domain since finite support in the time domain implies infinite support in the frequency domain (and vice versa).

Things are different if the function is periodic.