NMR spectrum of cyclohexanol - hints on integration
To answer your first question about measuring the integrals for the peaks between 1 and 2 ppm: If you seriously need to do a very accurate integral of these peaks without having access to NMR processing software (ie you've just been given the spectrum as a handout), you can resort to one of the methods of choice from the good 'ol days. 


Print your spectrum out on a nice big piece of paper, get a nice sharp pair of scissors and cut out your peaks and weight them (a 4 or 5 figure  balance may be required). These method gives incredibly accurate integrals
Print out your spectrum on graph/grid paper and count the grids. Again, very accurate, depending on the scale of grid you choose to print on.


As for 'pairing up' the remainder of the ring protons, this is not a trivial exercise, made even less so with the dispersion of the spectrum you are working with. You are quite right in your assessment. The protons closer to the -OH group will be at higher chemical shifts; equatorial and axial protons will be non-equivalent (equatorial at higher chemical shifts); and the whole fluxional ring dynamic will be temperature, concentration, solvent and field dependent. So, probably it is not worth trying to pair up any of these protons. You could (and hopefully would, if you are a thorough researcher) assign all of your peaks with the assistance of 2D COSY, HSQC/HMBC methods.