If α=1\alpha=1α=1 and β=1+i2\beta = 1 + \dfrac{i}{\sqrt{2}}β=1+2i, where i=−1i = \sqrt{-1}i=−1 are two roots of the equation x3+ax2+bx+c=0, a, b, c∈Rx^{3} + a x^{2} + b x + c = 0,\ a,\ b,\ c \in \mathbb{R}x3+ax2+bx+c=0, a, b, c∈R , then ∫−11(x3+ax2+bx+c) dx\int\limits_{-1}^{1} (x^{3} + a x^{2} + b x + c) \, dx−1∫1(x3+ax2+bx+c)dx is equal to :
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