In $\mathbb{R}$, any continuous function $f(x), a<x<b$, has an antiderivative: $$ F = \int_a^{x}f(t)dt, $$ In $\mathbb{C}$, a function $f(z)$ has an antiderivative only if it is entire (based on my understanding, please correct me if I am wrong).
This difference between the existence of an antiderivative in $\mathbb{R}$ and $\mathbb{C}$ is the source of my question:
My question is: In $\mathbb{C}$, is a function continuous if and only if it is entire (or, at least, analytic in its domain)?