Evaluate the following integrals

I_1 = \oint \vec{r} (\vec{a} \cdot \vec{n}) dS,
I_2 = \oint (\vec{a} \cdot \vec{r})\vec{n} dS,

where \vec{a} is a constant vector, and \vec{n} is an unit vector normal to the closed surface S.

I'm not sure whether the Stokes's theorem can be used in this case. For instance, if we write the integrals in the component notation

I_1 = \oint x_i (a_j dS_j),
I_2 = \oint (a_j x_j)dS_i,

then the Stokes' theorem would suggest the supstitution dS_i \to dV \partial_i where S=\partial(V). This results in

I_1 = \int (a_j \partial_j) x_i dV=\vec{a} V,
I_2 = \int \partial_i (a_j x_j)dV=\vec{a} V.

Is this correct?