The value of the integral $$\displaystyle{\int_{-\infty }^{\infty }\frac{\sin x}{x^2+2x+2}}dx$$ evaluated using contour integration and the residue theorem is
- $\displaystyle{\frac{-\pi \sin(1)}{e}}\\$
- $\displaystyle{\frac{-\pi \cos (1)}{e}} \\$
- $\displaystyle{\frac{\sin (1)}{e}} \\$
- $\displaystyle{\frac{\cos (1)}{e}}$