1)$\displaystyle \oint_{\mid z+1\mid =1}\frac{dz}{z^{2}-1}$

2)$\displaystyle \oint_{\mid z-i\mid =2}\frac{sin(\pi z)}{z^{4}}dz$

3)$\displaystyle \int_{0}^{\pi}\frac{d \theta}{2+cos(\theta)}$

4)$\displaystyle \int_{- \infty}^{\infty}\frac{cos(x)}{x^{4}+1}dx$

Can you please tell me how can I find the value of these integrals? Just tell me how.