Okay, I have a fairly stupid question.

How do I check wheter integral

$\displaystyle \int_{-\infty}^{\infty} f(x) dx$ exists?

When I have

$\displaystyle \int_{a}^{b}f(x)dx$, I have to check that f is bounded and continuous almost everywhere. Do I have to do the same when I have $\displaystyle <-\infty, \infty>$? Is it enough to do the same?

Thank you.