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Possible Duplicate:
Solving the integral $\int_{0}^{\infty} \frac{\sin{x}}{x} \ dx = \frac{\pi}{2}$?

How to prove $$\int^{\infty}_{0}\frac{\sin x}{x}\mathrm{d}x=\frac{\pi}{2}$$ Do you have a simple method ?

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marked as duplicate by user17762, J. M. is a poor mathematician, David Mitra, AD., davidlowryduda Apr 29 '12 at 5:31

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This is known as the Dirichlet integral. A couple of different derivations appear on the Wikipedia page:

http://en.wikipedia.org/wiki/Dirichlet_integral#Evaluation

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