Answer
$-g(x)$ and $g(y)$
Work Step by Step
Our aim is to take the first partial derivatives of the given function $f(x,y)$ with respect to $x$, by treating $y$ as a constant, and vice versa:
$f_x=\int_x^ y g(t) dt =- \int_{y}^{x} g(t) dt$
or, $\dfrac{\partial f}{\partial x}=-g(x)$
Our aim is to take the first partial derivatives of the given function $f(x,y)$ with respect to $x$, by treating $y$ as a constant, and vice versa:
$f_y=\int_x^ y g(t) dt $
or, $\dfrac{\partial f}{\partial y}=g(y)$
