We have two random variables X,Y with continuous dist. Its join density function is f(x,y) and marginals fX(x) and fY(y).

I need to show that the integral from -infinity to infinity with respect to y of the joint density function is the marginal fX(x), and the same with respect to x is the marginal fY(y).

I'm not sure where to start here. one thought was to start by showing how to get to the marginal dist function for a certain variable. Then from there we could differentiate to get the marginal density function we are looking for. Using this method seems correct, by I'm not sure what bounds to use.