  The Askey--Wilson integral is very important in the theory of orthogonal
polynomials. Liu's integral is a generalization of the Askey--Wilson integral
with many parameters. With the help of the series rearrangement method, we give
the elementary proof of them. Furthermore, we establish two new Askey--Wilson
type integrals in the similar way and find a generalization of a known
transformation formula containing three $_{3}\phi_{2}$ series.
