$$\int_{-a}^{a}{\frac{x}{x^6+i}}\,dx$$ where $i$ denotes the imaginary unit.
Let $f(x):=\frac{x}{x^6+i}$. Then $f(-x)=\frac{-x}{(-x)^6+i}=\frac{-x}{x^6+i}=-f(x)$. Therefore $f$ is odd and the integral equals zero $\forall a \in \mathbb{R}$.
Is that correct?