This is multi-part problem, starting with:

Consider the region in the first quadrant that is bounded above by $\displaystyle y=Ax-Ax^2$, and below by $\displaystyle y=3x$. A is the unknown parameter, which allows the above to be true, and should be considered a constant.

We are to write a definite integral for this, leaving the final answer in terms of A.

So, when graphing this, you can see that $\displaystyle y=Ax-Ax^2$ only goes from 0 to 1. I figured that this would mean that our definite integral would go from 0 to 1, but apparently this is wrong. The integral I got was

but, I guess the bounds should be from 0 to some number, say z. I understand that the bounds of integration are dependent on A, but I'm not sure how, exactly.

Any help would be great, I've been wracking my brain for a couple days on this problem.