Decision making in dynamic environments requires discounting old evidence that may no longer inform the current state of the world. Previous work found that humans discount old evidence in a dynamic environment, but do not discount at the optimal rate. Here we investigated whether rats can optimally discount evidence in a dynamic environment by adapting the timescale over which they accumulate evidence. Using discrete evidence pulses, we exactly compute the optimal inference process. We show that the optimal timescale for evidence discounting depends on both the stimulus statistics and noise in sensory processing. When both of these components are taken into account, rats accumulate and discount evidence with the optimal timescale. Finally, by changing the volatility of the environment, we demonstrate experimental control over the rats' accumulation timescale. The mechanisms supporting integration are a subject of extensive study, and experimental control over these timescales may open new avenues of investigation.