It is surprisingly hard to find information about the timing of neurons, in particular how long an action potential can contribute to the summation of a neuron. Is it on the order of milliseconds or seconds, i.e. for a neuron to fire, do many of the presynaptic neurons fire about at the same time?
Many of the neurons in the auditory system have voltage-gated low threshold potassium channels which allow neurons to maintain high firing rates and high temporal acuity. This makes the auditory system a good candidate for finding "fast" neurons. McGineley and Oertel (2006) looked at temporal integration in the ventral cochlear nucleus of the auditory system and found that the integration window was as low as 1.4 ms for octopus cells and of "unlimited" duration for T stellate cells.
I think, but I do not know how to calculate an integration window, that the cells of the Medial Superior Olive are even faster. These cells need to encode differences in timing between the ears on the order of 10s of microseconds.