Solution
= Solution
On the unit <sphere>, the outward <unit normal> is $\mathbf n=(x,y,z)^T$, so the normal component of the radial <vector field> is $\mathbf F\cdot\mathbf n=x^2+y^2+z^2=1$. The direct <surface integral> is
$$
\Phi=\int_0^{2\pi}\int_0^\pi1\cdot\sin\theta\,d\theta\,d\phi
=\boxed{4\pi}.
$$
Here $dS=\sin\theta\,d\theta\,d\phi$ is the unit-sphere <area element of a surface> in <spherical coordinates>.