If S={x ∈ R: sin^-1((x+1)/(√(x^2+2 x+2)))- sin^-1(x/(√(x^2+1)))=(π)/4}, then Σ_x ∈ s( sin ((x^2+x+5) (π)/2)- cos ((x^2+x+5) π)) is equal to ____.

If $\displaystyle S=\left\{x \in \mathbb{R}: \sin ^{-1}\left(\frac{x+1}{\sqrt{x^2+2 x+2}}\right)-\sin ^{-1}\left(\frac{x}{\sqrt{x^2+1}}\right)=\frac{\pi}{4}\right\}$, then $\displaystyle \sum_{x \in s}\left(\sin \left(\left(x^2+x+5\right) \frac{\pi}{2}\right)-\cos \left(\left(x^2+x+5\right) \pi\right)\right)$ is equal to $\displaystyle \_\_\_\_$.