How do I show the following,

If U is a smooth scalar field and N is a unit normal then

SSS grad(U) dV = SS (U)N dS (Note the S's at the beginning are integral signs.) ?

I have to apply the Divergence Theorem (Gauss' Theorem) to F=Uc where c is an arbitrary constant vector to get the above identity.

How do I go about solving this?