I'm currently studying Calculus from Stewart's book, and for the The Fundamental Theorem of Calculus Pt. 1, he defined a function $g(x) = \int_0^x f(t) dt$ which represented the area under $f(x)$ from $0$ up to $x$ and proved that $g(x)$ is the antiderivative of $f(x)$ and, in this case, if I plugged in an $x$ for $g(x)$, it would give me the area under the curve from $0$ til that $x$ since $g(x) = \int_0^x f(t) dt$
However, for an arbitrary function $f(x)$, if I found the antiderivative and plugged in an $x$, it would give me the area under the curve of $f(x)$ from which point upto $x$?