This was an equality written in p15, Titchmarsh,
$$ \int_0^{\infty} \frac{ \sin y }{y^{s+1}} \,dy = - \Gamma(-s) \sin \frac{1}{2} s \pi $$
How is this true? The RHS, by definition is equal to $$ \int_0^{\infty} \frac{ e^{-y} \sin \frac{1}{2} s\pi }{y^{s+1}} \,dy $$ which I do not see how it equates to the LHS.