  We present a computer algebra approach to proving identities on Bernoulli
polynomials and Euler polynomials by using the extended Zeilberger's algorithm
given by Chen, Hou and Mu. The key idea is to use the contour integral
definitions of the Bernoulli and Euler numbers to establish recurrence
relations on the integrands. Such recurrence relations have certain parameter
free properties which lead to the required identities without computing the
integrals.
