Measuring the distribution of a light sources intensity fluctuations is important to many scientific disciplines. However, these integrated intensity distributions are hidden in noisy experimental photon counting data because of the photometric detection process. Revealing integrated intensity distributions (RIID) without bias requires an approach that can account for a discrete, noisy and incompletely sampled data set without adding additional assumptions, approximations or otherwise arbitrary massaging of the data. I have developed a scheme using the maximum entropy method to uncover the integrated intensity distribution from the Poisson convoluted photon counting histogram. This technique can be extended to more complicated scenarios such as when a detector possesses dead time. The approach is demonstrated by revealing the integrated intensity distributions for several simulated photon counting data sets. In its present form, this procedure should be applicable to most classical photon counting measurements.