Surprised over notation in fundamental theorem So I'm looking into the fundamental theorem of calculus and I'm a bit weirded out by the notation used in part two. $$ \int_{a}^b f(t) dt = G(B)-G(a)$$ Why don't we say $F(b)-F(a)$? We are just talking about the anti-derivative of $a$ and $b$, right? !enter image description here

$G$ is any anti-derivative. The distinction here is important because if a function $f(x)$ has one anti-derivative $F(x)$, then $G(x) = F(x) + C$ is also an anti-derivative for $f$ for any constant $C$. So, there are many, and any one of them suffices to compute the definite integral $\int_a^b f(x)\;dx$.