Let $\mathbb{H}$ be the upper half plane in $\mathbb C$.
I was asked to describe the image of the function $f:\mathbb{H}\to \mathbb{C}$ defined by: $$f(z)=\int_{i}^z\frac{dw}{(w-1)^a(w+1) ^b}$$ where $a,b \in (0,1)$ and $a+b<1$.
Note: This is from a past graduate exam so I don't know what is the relevant background to solve this.