Calculating Volume of Revolution: Bounded Figure Rotated about y = -1

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What is the volume of the figure bounded by y = 2x - x^2, y = 2x, x = 2, and rotated about the line y = -1.

Is this the correct integral?

\[<br /> V = \pi \int_0^2 {((2x + 1)^2 - (2x - x^2 + 1)^2 } )dx<br /> \]<br />

Thank you for your time.
 
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Yes, your answer is correct.
 

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