HELP with my puzzlement in R. Jacob Baker's book!

I'm reading the book <<CMOS: Mixed-Signal Circuit Design>>.
When i come to page 186, i can not understand how comes the equation 32.42.
It said when the comparator change state, the output of the integrator changes by AT LEAST Gi*(Vdd-Vcm). [*???*]So the input of the integrator changes at least (Vdd-Vcm) .

But just let us assume: (Gi=1 for simplicity)
the current output of the integrator is 0.74, slightly less than Vcm ==> comparator output is 0==> assume the current input is 0.2 ==> the input of the integrator is 0.2-0=0.2 ===>next output of the integrator is 0.74+0.2 ====> as a result, the comparator CHANGE STATE to 1.5 ===> but if next input is 1.3 or something like that, the following change of the integrator input is only 0.2 (1.3-1.5).
Obviously, the change can not predicted by [*???*].

can any guy has this book help me with this?
Sorry for my poor English , thanks for any help

It is very straighfowrad: the author assumes in this example that the input barely changes from the previous cycle to the current cycle, when the comparator switches the state. Thus, if the input remains the same, you can easily determine your integrator output voltage change and thus, the conclusion of the comparator's hysteresis effect.