If α=1 and β=1+i √ 2, where i=√ -1 are two roots of the equation x^3+a x^2+b x+c=0, a, b, c ∈ R, then ∫_-1^1(x^3+a x^2+b x+c) d x is equal to:

If $\displaystyle \alpha=1$ and $\displaystyle \beta=1+i \sqrt{2}$, where $\displaystyle i=\sqrt{-1}$ are two roots of the equation $\displaystyle x^3+a x^2+b x+c=0, a, b, c \in \mathbb{R}$, then $\displaystyle \int_{-1}^1\left(x^3+a x^2+b x+c\right) d x$ is equal to: