Do the following integrals:

a. \(\oint_{|z-i|=3} \frac{e^{z}}{z^{2}+\pi^{2}} d z\)

b. \(\oint_{|z-i|=3} \frac{z^{2}-3 z+4}{z^{2}-4 z+3} d z\).

c. \(\int_{-\infty}^{\infty} \frac{\sin x}{x^{2}+4} d x\). [This is \(\operatorname{Im} \int_{-\infty}^{\infty} \frac{e^{i x}}{x^{2}+4} d x\).]