Complex Analysis: countour integral

[Bonjournoo]

Homework Statement

Compute the contour integral I around the following curve $\Gamma$:

$ I = \int_\Gamma \dfraq{dz}{z^2 +1} $

see picture:
http://dl.dropbox.com/u/26643017/Screen%20Shot%202012-01-07%20at%2010.39.58.png

Homework Equations

The Attempt at a Solution

$\Gamma$ is an open curve, but even if you close it with a line from A to B an the real axis, you may not use cauchy's theorem and calculate it with the residue theorem, because it is not a "smooth curve"...

 

[Dick]

The curve doesn't have to be "smooth" to apply Cauchy's theorem. It only has to be rectifiable. Piecewise smooth is plenty good enough.