$\displaystyle \int\limits_C \vec{F} .dS = ?$

$\displaystyle \vec{F} = (2xy, (1-y)z + x^2 + x, (x^2/2 + e^x)$

$\displaystyle C: x^2 + y^2 = 1$ intersection with $\displaystyle z^2 = x^2 + (y - 1)^2$

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The problem here is find the limits of integration. The rest I know how to do. I can find the equation of the curve C, but does it helps?