Let $f: D(0,1) \rightarrow \mathbb{C}$ be continuous and holomorphic on $D(0,1) \setminus \left]-1,1\right[$ such that for all $a,b,c \in D(0,1): \int_{[a,b,c,a]}f(z) \, dz=0$.
I have to prove that $f$ has a holomorphic primitive
What I did: I searched any theorems that could help. but I only found the contraposition: if $f$ has a holomorphic primitive then integration over any loop is 0.
Could you please help? Any hints much appreciated.
Many thanks!