Are you working with improper integrals?
After your integration, did you have something like this?
\(\displaystyle \lim_{b \to \infty} (2\tan^{-1}(b/2))\)
Because, yes, that does equal \(\displaystyle \pi\)
I'm hesitant in replying though. Subhotosh Khan is a lot smarter than me, and he doesn't like something. :?