What does it mean for resistance, as it appears in Ohm's law, to be an integral, evaluated over the body as a whole?

In literature I read:

The three linear flux laws mentioned are:

As seen, a correspondence exist between the hydraulic conductivity $K$, thermal conductivity $lambda$, and electrical conductivity $sigma$. In terms of electrical resistivity, $rho$, Ohm’s law could be written
$$-nabla V = rho vec i$$

I believe the differential equation being refered to in the last sentence is Fourier’s partial differential equation of heat conduction — the heat equation.

I do not know what are, or what is meant by, "integral equations and flow nets" in the last sentence (for which "Ohm’s law is inherently well suited").

So my questions are: What does it mean for resistance, as it appears in Ohm’s law, to be an integral, evaluated over the body as a whole? What are integral equations and why is Ohm’s law well suited for them? Why is Ohm’s law not well suited for the heat equation (the differential equation)?