Let a be a positive number. Evaluate the integrals $$\int_0^{\infty} \frac{1}{t^{4} + a^{4}} dt $$ and $$\int_0^{\infty} \frac{t^{2}}{t^{4} + a^{4}} dt $$ by integrating the function $({z^{2} + a^{2}})^{-1}$ in the counterclockwise direction around the boundary of the region {z : |z| $\leq$ R, 0 $\leq$ Arg z $\leq$ $\frac{\pi}{4}$ }, and taking the limit as R $\to$ ${\infty}$
I know I am supposed to use Cauchy's theorem for a convex region but not sure how to proceed