z = y^2
x = -2, x = 3
y = -1, y = 3
Sorry for being a nuisance, but i don't understand how we can find the limits for each integration, as i cant sketch a 3d graph?
$\displaystyle z= y^2$, in three dimensions, is a "parabolic cylinder". Imagine a parabolic "trough" running along the x-axis.
In fact I would recommend graphing the parabola $\displaystyle z= y^2$ on yz-axes. With positive y to the right and positive z upward, the positive x-axis is coming out of the paper toward you. Draw the vertical lines y= -1 and y= 3 (they are actually planes coming out of the paper toward you and away from you). x= -2 is the plane parallel to the paper and behind it, x= 3 is parallel to the paper and in front of it.
However, what you have given is NOT a closed region. You have x= -2 and x= 3 as front and back boundaries and y= -1 and y= 3 as left and right boundaries but you need some other condition on z to have a top or bottom boundary.