I have come across some complex integrals with limits when doing questions but have not been able to make sense of what they mean due to my lack of understanding.
We usually define integrals along a path and I have been told that taking a suitable parameterisation is a good way to evaluate these integrals. There are other approaches like using Cauchy's Integral formula etc.
However I saw a definite complex integral written and wanted to make sense of such a thing: what would the following signify? $$\int^i_{1+i} z \, dz$$
My best guess is that this is an integral over the path joining the line $1+i$ to $i$. Could this also represent any path joining these two points in this case? If I were to choose a function that isn't entire like $f(z)=z$ then what would the integral mean?