If I have:
$$f(x,y)=\int\_{x}^{y}e^{-t^2}dt$$
To calculate that, I change the t to y and x to get:
$$e^{-y^2}(e^{-y^2})'-e^{-x^2}(e^{-x^2})$$
With the differentials being in respect to x and y for each partial derivative?