Double Integration Check: Evaluating a Double Integral for a Triangle

[tomeatworld]

More of a check

Homework Statement

Evaluate $$\int\int (x^{2}(y+1) + e^{y})$$ for a triangle with vertices at (0,0) (1,1) (-1,1)

Homework Equations

Integration

The Attempt at a Solution

The only this I wanted to check, is that integrating the square at y=0 to 1 and x=0 to 1 will give the correct answer (as the triangle is reflected on the y axis) and if not, how you get the limits.

 

[Mark44]

I don't see how "integrating the square at y = 0 to 1 and x = 0 to 1" relates to this problem, even if it happens to produce the right answer.

If you integrate first with respect to x and then with respect to y, your limits of integration will be x = - y to x = y, and then y = 0 to y = 1.