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