We can measure the accumulation of some function by the area under its graph. We call this integration.
Integration is the opposite of differentiation.
If a function F shows the accumulated values of f, then f is the rate of change of F, and vice-versa. We can estimate the area under a curve by adding the areas of rectangles. If the heights of the rectangles always stay below the curve we get an underestimate of the area. If the heights of the rectangles always stay above the curve we get an overestimate of the area. For any continuous function, there is exactly one number that satisfies the above condition.