Volume of a solid of revolution, changing orientation

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I am having trouble getting through this problem, been working on it for quite some time and getting nowhere. The problem is as follows:

Find the volume of the solid obtained by rotating the region bounded by the two curves about the y axis.

$$x = y-y^{2}$$ $$x=0$$

I changed the curves to the following(and rotating them about the x axis):

$$c(x) = x - x^2 $$ $$ y = 0 $$

I then set area equal to: $$A(x) = \pi (c(x))^2 $$ From here, shouldn't I be able to do the following to find the volume? If this is wrong, why is it wrong?

$$V = \int_0^1 A(x)dx\ $$

Thanks in advance!