Fundamental theorem of calculus along a line segment
= Fundamental theorem of calculus along a line segment
If $f:U\to\mathbb R^m$ is continuously differentiable and the segment from $x$ to $y$ lies in $U$, then
$$
f(y)-f(x)=\int_0^1Df(x+t(y-x))(y-x)\,dt.
$$