I want to use the formula of Stokes to calculate the integral $\iint_{\Sigma}(\nabla \times f)\cdot N \ dA$ for the function $f(x,y,z)=(-y+xz+yz^2, x+xyz^3, x^2z^4)$ when $\Sigma$ is the union of the surfaces that are defined by the relations $x^2+y^2=1$ and $0\leq z\leq 1$ and the surface that is defined by $x^2+y^2+(z-1)^2=1$ and $z\geq 1$ and the normal vector of $\Sigma$ direct to the z-axis.
$$$$
From the formula of Stokes we have that $$\iint_{\Sigma}(\nabla \times f)\cdot N \ dA=\oint_{\sigma_1}f\cdot d\sigma_1+\oint_{\sigma_2}f\cdot d\sigma_2$$
When we calculate the curve integral at the boundary do we consider a clockwise or an anticlockwise parametrization?