Greens theorem over a trapezoid

Question

This is the solution to a problem on greens theorem bounded by a trapezoid. I am stuck on the third last equality sign. I suspect it has to do with symmetry of the domain but can not see how it has been applied. Appreciate it if someone could clarify it for me.

Answer 1

We have:

$$ \int \int _T (3+2y)dA=\int \int _T 3dA+\int \int _T 2ydA $$

and,

$$ \int \int _T 2ydA=\int_0^1dx\int_{-2+x}^{2-x}2y dy=\int_0^1 [(2-x)^2-(x-2)^2]dx=0 $$