High-throughput real-time optical integrators are of great importance for applications that require ultrafast optical information processing, such as real-time phase reconstruction of ultrashort optical pulses. In many of these applications, integration of wide optical bandwidth signals is required. Unfortunately, conventional all-optical integrators based on passive devices are usually sensitive to the wavelength and bandwidth of the optical carrier. Here, we propose and demonstrate a passive all-optical intensity integrator whose operation is independent of the optical signal wavelength and bandwidth. The integrator is implemented based on modal dispersion in a multimode waveguide. By controlling the launch conditions of the input beam, the device produces a rectangular temporal impulse response. Consequently, a temporal intensity integration of an arbitrary optical waveform input is performed within the rectangular time window. The key advantage of this device is that the integration operation can be performed independent of the input signal wavelength and optical carrier bandwidth. This is preferred in many applications where optical signals of different wavelengths are involved. Moreover, thanks to the use of a relatively short length of multimode waveguide, lower system latency is achieved compared to the systems using long dispersive fibers. To illustrate the versatility of the optical integrator, we demonstrate temporal intensity integration of optical waveforms with different wavelengths and optical carrier bandwidths. Finally, we use this device to perform high-throughput, single-shot, real-time optical phase reconstruction of phase-modulated signals at telecommunications bit rates.