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Integrating over a closed contour following vector field

Integrate over a closed contour $c$ $$\oint_c d\vec{r}\times\vec{a}, \quad \vec{a}=-yz\vec{i}+xz\vec{j}+xy\vec{k}$$ where $c$ is cross-section of following two surfaces $$x^2+y^2+z^2=1$$ and $$y=x^2$$ ...