I am studying line integrals and I came across this formula:
$$ \operatorname{Area}(\Sigma) = h\,l(C) = \int_a^b f(\gamma(t)) \left\| \gamma'(t) \right\| dt = \int_\gamma f. $$
It's clear that the area is $height \cdot base$, but isn't it all included in $\int_a^b f(\gamma(t))$, since the integral gives the area under a specific function?