integration - How can I evaluate $int_0^infty frac{sin x}{x} ,dx$? [may be duplicated]

How can I evaluate $\displaystyle\int_0^\infty \frac{\sin x}{x} \, dx$? (Let $\displaystyle \frac{\sin0}{0}=1$.)

I proved that this integral exists by Cauchy's sequence.

However I can't evaluate what is the exact value of this integral.

Answer

It's a famous Dirichlet integral.
http://en.wikipedia.org/wiki/Dirichlet_integral