  We describe the utility of integral representations for sums of basic
hypergeometric functions. In particular we use these to derive an infinite
sequence of transformations for symmetrizations over certain variables which
the functions possess. These integral representations were studied by Bailey,
Slater, Askey, Roy, Gasper and Rahman and were also used to facilitate the
computation of certain outstanding problems in the theory of basic
hypergeometric orthogonal polynomials in the $q$-Askey scheme. We also
generalize and give consequences and transformation formulas for some
fundamental integrals connected to nonterminating basic hypergeometric series
and the Askey--Wilson polynomials. We express a certain integral of a ratio of
infinite $q$-shifted factorials as a symmetric sum of two basic hypergeometric
series with argument $q$. The result is then expressed as a $q$-integral.
Examples of integral representations applied to the derivation of generating
functions for Askey--Wilson are given and as well the computation of a missing
generating function for the continuous dual $q$-Hahn polynomials.
