I'm going through a complex analysis question that says : Let $R$ be a positive real number greater than $2$, let $γ_1\colon[−R,R]\longrightarrow\mathbb{C}$ be defined by $\gamma_1= t$, let $\gamma_2= S(0,R)$ and let $\gamma=\gamma_1\oplus\gamma_2$. By using Cauchy’s Residue Theorem show that $$\int_\gamma\frac{z^2}{(z^2+1)^2}\mathrm dz = \frac{\pi}2$$

After going through the problem I can see that the two poles for $z$ are $\pm i$. However in the answer it says that only $i$ is in $\gamma$. I was wondering what does $\gamma$ mean in this context, and why does it only allow $i$ to be a pole.