Hi again,
R2 has to be larger than R1 for at least this one following reason:
When point B is low it is at -5v, and that means point A is going high heading toward +5v. We will first assume R1=R2 just to illustrate.
Now before point A gets to +5v, we have a negative voltage at point C, which can certainly not trip the comparator output to a high state (which we need to happen for oscillation to occur).
Now once point A finally reaches +5v, that is the maximum it can get to (assuming a perfect rail to rail output integrator), and because R1=R2 that puts exactly 0v at point C, which is still not enough to trip the comparator (assuming even a tiny tiny offset of 1nv). That means that the circuit will never oscillate when R1=R2 unless we get lucky with the offset or the resistors are really slightly different and R2>R1.
Now lets look at the same state when R1>R2.
With R1 larger than R2 the voltage drop across R1 will be greater than across R2, so point C will never be able to get above zero to trip the comparator.
Point C will always remain negative and we're stuck.
Now lets make R2>R1.
With R2>R1, at some point, point A will be high enough to cause a level at point C that is higher than ground (0v) and that will force the output of the comparator high, which is what we need. The output goes high, and that starts the integrator ramping down, and the process repeats only with the polarities reversed.
So the conclusions are:
With R1>R2 there will be no oscillation.
With R1=R2 there may be oscillation but only if we get lucky.
With R1<R2 there should be oscillation always, as long as point A can reach a high enough voltage (which may be limited by a real life op amp) or the resistors are sized to work with a lower output.
Numerically, R1=10k and R2=20k look like a good choice because that would allow switching when point A is at either 2.5v or -2.5v which seems comfortable, however you really have to check the particular op amp being used to make sure it's output can get up as high as 2.5v with only a +5v supply, and down to -2.5v with only a -5v supply.
It's also a good idea to check the input ranges for the op amp and comparator to make sure they are within the range of the actual devices used in the real life circuit.