Where $\Omega_s$ is new integration region, due to change in geometry integration region will also change.
Also note that $\Omega_l$ is $\Omega$ with $|x|<l$ is the integration region for $\Omega_l$ in $z-plane$. If $\Omega_s$ is the image of $z$ under mapping, so what will be the integration region for $\Omega_s$ in $\omega-plane$?
Also check the figure for more detail.
