I assume by integration, you mean a running estimate of the integral of a signal (e.g. from 0 to the current point): $\int_0^t f(\tau) d\tau$.
Methods like Savitzky-Golay filters are needed to differentiate noisy signals because naive methods like finite differencing are very sensitive to noise. In contrast, integration inherently provides smoothing, so there's not as much need for specialized methods. One can sometimes get away with really simple approaches, like taking the cumulative sum over elements of the signal vector, multiplied by the sampling interval.
One way to think of this is that the finite difference estimate of the slope only depends on a couple points. The noise can completely dominate this estimate if the magnitude of the noise is large relative to the actual change in signal between the points. In contrast, integration requires summing over many previous points. To the extent that noise fluctuates up and down rapidly relative to the signal, it will average out.
For example, here's a signal with additive white Gaussian noise, integrated by the simple cumulative sum method mentioned above. The integral of the noisy signal matches the true value fairly well, without any special treatment.
Of course, the nature of the noise matters, and it my be necessary to explicitly filter it out in some cases. For example, if the signal is contaminated by high amplitude, low frequency noise, this could heavily influence the integral (but wouldn't affect the derivative as much). So, it would be best to apply a high pass filter before integrating. If the noise is narrow band (e.g. 50/60Hz noise from the power lines), a notch filter would be appropriate, etc.