I'm having trouble interpreting the four dimensional version of Gauss' law. In the original version, a vector would be integrated around a closed 2D surface and this would be equal to the integral of divergence over the enclosed volume. In the newer version, the vector(or tensor) is integrated over a 3D hypersurface and this is equal to the integral of the covariant derivative over the 4D volume. Now, how could the integral over a bounded 3D volume be equal to the integral over an unbounded 4D volume? I mean, how could the integral over a fixed 3D volume be equal to the integral over 4D volume that is carried on forever in time?