Answer
$4$
Work Step by Step
Re-arrange the given integral as follows:
$\int_{0}^{2}[xy-y^2)_{-1}^{1}]dx=\int_{0}^{2}[(2x) (x-1+x+1) dx$
This implies that
$\int_{0}^{2} 2x dx= (2^2-0^2)$
Thus, we have, $4-0=4$
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