We demonstrate multiphoton discrimination at a telecommunications wavelength with the readout frequency of $40\mathrm{Hz}$ by a charge-integration photon detector (CIPD). The CIPD consists of an InGaAs pin photodiode and a GaAs junction field effect transistor as a preamplifier in a charge-integration circuit, which is cooled to $4.2\mathrm{K}$ to reduce thermal noise. The quantum efficiency of the CIPD (the detector itself) is 80% for $1530\mathrm{nm}$ light, and the readout noise is measured as 0.26 electrons at $40\mathrm{Hz}$ . We can construct Poisson distributions of photocarrier numbers with distinct peaks at each photocarrier number, corresponding to a signal-to-noise ratio of about 3.