TD

@ Dave, Mathworld is correct but it included these kind of improper integrals.

An improper integral is a definite integral that has either or both limits infinite or an integrand that approaches infinity at one or more points in the range of integration.

The bold part includes the integrands with, for example, zeroes of the denominator so vertical asymptotes.

@ ecoli: no, the integral isn't considered as improper then