@modus_ponens
Yes, this is Cauchy’s integral formula, the contour is closed since it is the boundary of Omega. The only assumptions needed are that Omega must be a simply connected open subset (or an open star domain) of C, f is holomorphic over Omega and z is in the interior of Omega.

Oh, she’s so cute! But these terrible integrals and symbols make me shiver all over my body. How I did not like mathematics lessons and tried my best to skip them. Once we had a very tricky topic and I came across https://plainmath.net/post-secondary/calculus-and-analysis/integral-calculus/conic-sections where I could find free solutions to conic sections equations - probably one of the most difficult topics for me that we had to study. In general, I’m definitely not a fan of this science, but I have always enjoyed learning physics.

Hjalp! Fell asleep during the lecture! What integral is that? Its appearance is screaming to have “Cauchy” written all over it. Ah hmm, is it Cauchy’s integral formula? But wait, is the contour closed here? Also, do we assume the function to be holomorphic? Aaa daamn… going to struggle bad with home exercises this time.