Code

<<Graphics`FilledPlot`

RiemannSum[f_,{a_,b_,n_},proportion_:(1/2)]:=
Module[{h=(b-a)/n,p=1-proportion,s},s=Sum[f[a+(i-p)h],{i,1,n}];h*s]

LeftEndpointRule[f_,{a_,b_,n_}]:=RiemannSum[f,{a,b,n},0]
RightEndpointRule[f_,{a_,b_,n_}]:=RiemannSum[f,{a,b,n},1]
TrapezoidRule[f_,{a_,b_,n_}]:=
    (RiemannSum[f,{a,b,n},0]+RiemannSum[f,{a,b,n},1])/2
MidpointRule[f_,{a_,b_,n_}]:=RiemannSum[f,{a,b,n},1/2]
SimpsonRule[f_,{a_,b_,n_}]:=
    (TrapezoidRule[f,{a,b,n}]+2*MidpointRule[f,{a,b,n}])/3