Find the area bounded by the curves x = y2 - 4y and x = 2y - y2. your work must include an integral in one variable.

The curves x = y^2 - 4y and x = 2y - y^2 are two parabolas with vertices (-4,2) and (1,1), respectively.

The solutions (0,0) and (-3,3) of system give the common points of these parabolas.
The area is calculated in the image.

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