This paper studies intertemporal choice in a dynamic framework with continuous time. A model called continuous quasi-hyperbolic discounting is considered, extending the popular quasi-hyperbolic discounting to an integral form. Dynamic preference axioms, time consistency and time invariance, are formulated and used to provide a foundation for an integral form of exponential discounting; the central model of dynamic, intertemporal choice in economics. A relaxation of the time consistency axiom, complementary time consistency, is formulated to provide a dynamic preference foundation for continuous quasi-hyperbolic discounting. A preference condition for present bias is also characterised in the context of the model.