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$\int_{-1}^1\left(a x^3+b x\right) d x=0$ for
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The correct answer is:
any value of $a$ and $b$
$\begin{array}{r}\int_{-1}^1\left(a x^3+b x\right) d x=\left[a \frac{x^4}{4}+b \frac{x^2}{2}\right]_{-1}^1 \\ =\frac{a}{4}(1-1)+\frac{b}{2}(1-1)=0\end{array}$
For any value of $a$ and $b$.
For any value of $a$ and $b$.
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