We present the results of the detected voltage distribution of a quantum random number generator (QRNG) based on a photonic integrated circuit comprising a semiconductor laser, delay interferometer and photodetector. We find that the integrated QRNG system behaves as expected for a QRNG from discrete gain-switched laser sources, especially exhibiting all of the peculiarities of the random voltage distribution and behaving as previously demonstrated for a discrete optical component setup. The biggest advantage of having all of the components integrated into a single chip is that only electrical connections are needed to operate the system, without the need for tricky and expensive optical alignment to external circuitry. We supply results showing that a random bit stream created from the random numbers passes the NIST statistical test suite tests, thus demonstrating the feasibility to generate random numbers via quantum means at gigabit/s rates from a single photonic integrated circuit. All of our results are backed by numerical simulations.