Fundemental theorem of Calculus intuition

[Alex K]

It's more intuitive if you look at it the other way around - If you look at how the integral function F (as a function of the upper bound of the integral) arises geometrically as the area under the curve f, I find it very intuitive that the rate of change of the function F is given by the height of the graph of f. The larger f is at a point, the quicker the area, and hence F, increases when integrating a bit further.