What are integration scale and differentiation scale?
The $\sigma_I$ determines the scale level at which the Harris corners are computed. Coarser scales (higher values of $\sigma_I$) correspond to larger corners.

The $\sigma_D$ is effectively the window size, over which the derivatives are summed to generate the entries of the matrix. If $\sigma_D$ is too small, then the detector will be seriously affected by noise.  If it is too large, then small corners may wash out.  In the original non-scale-adapted Harris detector you only have $\sigma_D$.

By the way, this is the first time I see the terms "integration scale" and "differentiation scale", and I am not sure I like them. The "differentiation scale" is actually the Gaussian envelope, over which the derivatives are integrated. :)