All-optical integrators are key devices for the realization of ultra-fast passive photonic networks, and, despite their broad applicability range (e.g., photonic bit counting, optical memory units, analogue computing, etc.), their realization in an integrated form is still a challenge. In this work, an all-optical integrator based on a silicon photonic phase-shifted Bragg grating is proposed and experimentally demonstrated, which shows a wide operation bandwidth of 750 GHz and integration time window of 9 ps. The integral operation for single pulse, in-phase pulses, and π-shifted pulses with different delays has been successfully achieved.