  In this paper, we derive a formula on the integral of products of the
higher-order Euler polynomials. By the same way, similar relations are obtained
for $l$ higher-order Bernoulli polynomials and $r$ higher-order Euler
polynomials. Moreover, we establish the connection between the results and the
generalized Dedekind sums and Hardy--Berndt sums. Finally, the Laplace
transform of Euler polynomials is given.
