Carroll and Ostlie write, in their book An Introduction to Modern Astrophysics (second edition), at the page 33, right after deriving Newton's Law of Universal Gravitation for two point masses using Kepler's third law and the three laws of motion :
Newton's law of gravity applies to any two objects having mass. In particular, for an extended object (as opposed to a point mass), the force exerted by that object on another extended object may be found by integrating over each of their mass distributions.
My question is : how is the integrating process a "particular" case of the formula for two point masses ? Shouldn't the integrating process really be a postulate on its own ?