You can set the integrand [math]f(x)[/math] (this only works for functions with nonnegative values).[br][br]Drag the points a and b to set the bounds of integration, and select the number of subintervals using the slider [math]n[/math].[br][br]The "random sample area" is a Riemann sum with uniform width [math]\frac{b-a}{n}[/math], and heights determined by picking a random value in each subinterval. The other three areas are the standard Riemann sums.[br][br]Click each tickbox to display or hide the rectangles corresponding to each sum.