As the title says, I am trying to find the definite integral of sech(x) with limits of infinity and minus infinity.

I always get 2pi as my solution, but all calculators and integration applets give pi as the answer.

Below is my method so far:

Could someone please tell me where I have gone wrong?

EDIT: there is an error in line 6 of my method, that extra u is just a typo.