Can an indefinite integration of a real function with respect to real variable have a complex integral constant? i.e. for $\int f(x) dx = g(x) + c$, can '$c$' be complex, where $f(x)$ is a real function?
N.B. As per as I understand, it can't have complex constant, because integration of a real valued function would only be defined on real plane. Am I right?
N.B. I am just checking my understanding. I need to use this result in another problem.
Thanks in advance. :)