The integral form and the differential form

It is well known that Maxwell's equations of electro-magnetism have an
integral and a differential form, which are usually considered
equivalent. I have realised that this can not be so.

Charge, after all, is quantised, and the derivatives therefore are all
either zero or infinite. Therefore the differential equations can only
be an approximation, while the integral forms are exact. This can also
be checked by noting that the integral form can be proven from the
differential (divergence theorem etc.), while going the other way
requires an assumption of continuity.

Matter, like charge, is discrete and not continuous, so the same must
be true of Einstein's equation of general relativity. If it can not be
written in an integral form, it is wrong !! Can it be? (I imagine one
would have to use the flat-spacetime formulation, which would itself
be interesting in suggesting that spacetime really is necessarily
globally flat.)

Andrew Usher