For decreasing f(x) the area of a right Riemann rectangle is less than the area under the curve i.e. the value of the integral. For an increasing f(x) the area of the rectangle is greater than the area under the curve i.e the value of the integral. The left and right Riemann rectangles can be compared on this page.

Approximating Integrals

A large number of rectangles can be used to approximate an integral (area under the curve), this is shown below: