Often you want to calculate the electric field of a lot of charges or the center of mass for a lot of small masses. When we have a rigid body or something similar in the world of electrodynamics, my book tells me always to calculate the cm or total field as an integral, because "the distributions are continous". Now I have always speculated about this line "they are continous". Because in this world everything is discrete. So isn't it just an approximation when you replace the sum of a hell of alot of elements with an integral?