Partial Derivatives and the Fundamental Theorem of Calculus I am being asked to evaluate the 1st-order partial derivatives $-$ $f_{x}$(x,y) and $f_{y}(x,y)$ $-$ of the following multi-variable function: $f(x,y) = \int_{y}^{x} cos(-1t^2 + 3t -1) dt$. Any help is appreciated.

$$
f(x,y)=\int_y^x g(t) dt=G(t)|_y^x=G(x)-G(y) \text{ where } G'=g
$$
so differentiating w.r.t $x$ on both sides of $f(x,y)=G(x)-G(y)$ gives
$$
f_x(x,y)=(G(x)-G(y))_x$$
and by difference rule that is
$$
f_x=(G(x))_x = g(x).
$$
