Q:

Find $\iint_Ty^2dxdy$, where T is the triangle with vertices at (0,0),(2,2) and (3,0)

I have a feeling I am meant to split the integrals, but I am struggling to work out which limits to set for my integrals.
I think it should be something like:
$\int_0^x\int_0^2y^2dxdy + \int_0^?\int_2^3y^2dxdy$
I'm not sure what the "?" is meant to be, so if anyone could show me:

Whether I am on the right track?
How they have actually worked that "?" out?
And finally, what to do no next, and how they've gotten their answer.

I'd be awfully greatful!

A:

Let $O = (0,0), A = (2,2), B = (3,0)$. The equation of the line that passes through $O,A$ is: 
$y = x$, and the equation of the line that goes through $A, B$ is: $y = -2x+6$. Thus:
$I = \displaystyle \int_{0}^2 \int_{y}^{\frac{6-y}{2}} y^2dxdy$

