Question

Evaluate the following integrals with the use of the Cauchy residue theorem.

∫(sin²x/x²)dx for x [- ∞, ∞] 

Answer 1

Since the integrand is an entire function, we deform the contour and get

where c is a contour in the upper half-plane joining −∞ and ∞. The first two terms in the integrand give zero. We get