Evaluate the integral (from -infinity to infinity) of cos(x)/(1+x^2).

I did it using Mathcad.  However, in WolframAlpha you can enter the following: int cos(x)/(1+x^2), x=-inf, x=inf to get the same thing.  I'm still thinking about how to do it by hand!

$${\frac{{\mathtt{\pi}}}{{\mathtt{e}}}}$$

Thanks Alan,

Did you get that straight off a calc?  

If not, how did you do it?

If so, which calc did you use?

I had a look at Wolfram Alpha but I didn't know how to enter a definite integral.

Thanks Alan