We demonstrate a photonic RF integrator based on an integrated soliton crystal micro-comb source. By multicasting and progressively delaying the input RF signal using a transversal structure, the input RF signal is integrated discretely. Up to 81 wavelengths are provided by the microcomb source, which enable a large time-bandwidth product of 81. Our approach also features a high degree of reconfigurability. By simply adjusting the value of dispersion (i.e., the length of dispersive fibre), the integration time window and resolution can be reconfigured to accommodate a diverse range of applications. We employed 13 km of standard single-mode fibre to achieve a large integration time window of similar to 6.8 ns, a time resolution as fast as similar to 84 ps, with a broad bandwidth of 11.9 GHz. In addition, we perform signal integration of a diverse range of input RF signals including Gaussian pulses with varying time widths, dual pulses with varying time intervals and a square waveform. The experimental results show good agreement with theory. These results verify our microcomb-based integrator as a competitive approach for RF signal integration with high performance and potentially lower cost and footprint.