Hi all!

So, I have a question regarding integration by parts, and I think it's pretty straight-forward, but it's bugging the hell out of me...

Supposing I have an integration $\displaystyle \int_{x_1}^{x_2}f(x)g(x)dx$, and integrate by parts, I'd have $\displaystyle \left[f(x)\int g(x) dx\right]_{x_1}^{x_2} - \int_{x_1}^{x_2}\frac{df(x)}{dx}\int g(x)dxdx$...

But, should there not be a boundary on the $\displaystyle \int g(x) dx$ terms? If so, what would they be? It just seems odd to me, but I'm probably overlooking something.