The question was stated as follows,
Evaluate the following double integral;
$$ \iint_R x^3y dA $$
where R is interior of triangle with vertices (0,0), (1,0), & (1,1) .
I thought for these types of double integrals I could have the limits in either of the two formats below;
$$ \int_0^1\int_0^y x^3y dxdy $$ 
$$ \int_0^1\int_0^x x^3y dydx $$ 
However the answer sheet states that the answer for only the latter integral is correct.
How can I set up or visualize the problem in order to set it up in the correct way?
I did plot the points on a graph, and got my y=x "limit" from there, I just cannot understand why  is the correct integral, and how to go about making sure that in every double integral problem, I choose the correct integral set up.
All help is much appreciated :)