You have to use use a reference standard, such LaB6, whose diffraction line broadening is negligibly affected by microstrain and size contributions.

In practice diffraction patterns of both the standard and the sample are collected using the same experimental conditions (sample holder, 2_theta step,...).

Then you analize the diffraction pattern of the standard in order to determine the U, V and W parameters of the Caglioti equation (this can be done by Rietveld refinement or a Le Bail plot).

The so-obtained values give the contribution of the instrumental broadening.

Concerning the integral breadt: The integral breadth can be treated like the FWHM. For a e.g. pseudo-Voigt (pV) function you can always calculate the integral breadth from the FWHM and the shape parameter of the pV. Then the shape can be described by the ratio of the FWHM and the integral breadth. The formulas have been distributed in some papers by Delhelz and Mittemeijer in the early 1980s which I have cited in J. Appl. Cryst. (2004). 37, 123–135. Note that (i) the separate treatment of Gauss and Lorentz like contibutions to the profile can be treated for convolution in the usual way (quadratic and linear difference), (ii) the treatment in J. Appl. Cryst. (2004). 37, 123–135 takes some detours. (iii) some formulas are only approximate.

Method is same for both integral breadth (IB) and FWHM. If you can correct instrumental broadening contribution for FWHM approach, use same formula for IB approach (for pV case IB > FWHM). Use same multiplier factor as used for converting FWHM to IB from XRD data i.e. FWHM = multiplier x IB. Originally Caglioti formula was proposed for pure Gaussian case, for which multiplier = ~ 0.94. Likewise for pure Lorentz case it is ~ 0.64. Other details are suggested by Prof. Andreas Leineweber.

For a long-term solution, I sincerely recommend the preprint article at link DOI: 10.13140/RG.2.2.27720.65287/3 or at link https://www.researchgate.net/publication/352830671.