  We show how the continuous Almkvist-Zeilberger algorithm can be used to
efficiently discover and prove differential equations satisfied by generating
functions of sequences defined as integrals of powers of C-finite polynomial
sequences (like the Chebyshev polynomials) from which one can automatically
derive linear recurrences with polynomial coefficients for the sequences
themselves. We fully implement this with a Maple package, CfiniteIntergal.txt .
