The classic integrability problem asks (i) what conditions guarantee that demand functions can be rationalized by a well-behaved utility function and (ii) if such a utility exists, how can it be recovered. Hurwicz and Uzawa (1971) provided answers to both questions. However for the popular case of changing tastes, as represented by a sequence of non-nested utilities, the Hurwicz and Uzawa conditions fail to hold in general. Following Strotz (1956), an individual can determine her dynamic demands via a naive or sophisticated solution technique. For given dynamic demands, we provide necessary and sufficient conditions such that the demands are rationalized by a set of utilities using the sophisticated solution process. Moreover we provide a means for recovering the generating sequence of utilities, although this sequence of utilities is not unique. We also give sufficient conditions for demands to be rationalized by a sequence of utilities using the naive solution process and for recovering the complete set of generating utilities for two special cases.