Visual Calculus http://archives.math.utk.edu/visual.calculus/4/ftc.9/ states $$A(x)=\int_{0}^{x}f(t)dt $$ is "an indefinite integral or antiderivative of f".
Whereas https://en.wikipedia.org/wiki/Antiderivative says $$F(x)=\int_{0}^{x}f(t)dt $$ is "the definite integral of f with variable upper boundary".
Which is correct?
Both are correct. Using the definite integral with a constant lower limit and the variable as the upper limit results in one particular indefinite integral/antiderivative.