The problem i came across is the evaluation of $$\int_0^\infty\frac{\sin x}{x}\,dx$$ I chose the function $f(z) = \dfrac{e^{iz}}{z}$ and took a contour of $[\varepsilon , R ] + [R , R+iy] + [-R+iy , R+iy] + [-R,-R+iy]+[-R, -\varepsilon]$ . The problem is how do I continue now to find integrals on each of these segments ?
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