The following example on file exchange (MATLAB Central) is one implementation of the Simpson's rule integration:
After you download the function, add it to your path and run the following code snippet:
numSamplePoints = 1000;
I = zeros(numSamplePoints,1);
for samplePoints = 1:numSamplePoints
% samplePoints
I(samplePoints) = simpsons(@(x)sin(x.^3),0,2*pi,samplePoints);
end
plot(1:samplePoints,I);
This will give you a plot showing the convergence of the integral vs. the number of samples used for the integration as shown below:
