Here is a note on deriving the formula for the sum of squares which we used in class to compute the Riemann sums for the area under a parabola.
Here is a MATLAB m-file to compute Riemann sums.
Here is a MATLAB m-file that plots a numerically computed antiderivative
Here is a MATLAB m-file that plots a parametric curve
Here are some pages reproduced from an English translation of Measurement of a Circle by Archimedes (c. 287 BC – c. 212 BC)
Here are some notes by an MIT student James Silva that explain some things about Bernoulli polynomials and their connection with sums of powers.