Riemann sums and definite integral

Import any continous function f(x) and lower, upper limits. Check the subinterval of interval [α,β], random choise of [math]ξ_κ[/math] , values of [math]f(ξ_κ)[/math] and Riemann recatngles. As pointer is moving from left to right the partitions get finer and the limit of the Riemann sums is the Riemann integral.