In my textbook, it states the fundamental theorem of calculus as follows: If $f(z) $ has an antiderivative $F(z)$, then $\int^{z_2}_{z_1} f(z)dz=F(z_2)-F(z_1)$.
There isn't a definition of what an antiderivative is anywhere; and it seems confusing to be defining the relation between derivatives and integrals using the relation itself (if that makes sense). What is an antiderivative?
Antiderivative is the function that, when derivated, yields the function of wich it is antiderivative. And integral function is the function that gives you the value of the integral, wich is a limit of sums.