Could someone help me through this problem?
Let C be an arc of the circle $|z|=R$, with $R>1$ of angle $\frac{\pi}{3}$.
Show that $\left|\displaystyle\int_{C} \frac{1}{z^{3}+1}\, dz\right|\leq \dfrac{\pi}{3}\left(\dfrac{R}{R^{3}-1}\right)$
and deduce $\lim\limits_{R \to{+}\infty}{\displaystyle\int_{C} \frac{1}{z^{3}+1}\, dz}$