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.

Apply Leibniz rule in each case. 
For example
$$
f_x(x,y){}={}\dfrac{\partial}{\partial x}\int\limits^{x}_{y}\cos\left(-t^2+3t-1\right)\mathrm d t{}={}\cos\left(-x^2+3x-1\right)\dfrac{\mathrm d}{\mathrm d x}x{}={}\cos\left(-x^2+3x-1\right)\,.
$$
