You said, "output swing btw ±5V" and " v1 is ±0.5Vcc".
I conclude that this means vcc=10V.
Arbitrarily set Ri=10k.
VN=0 (Do you understand the concept of "virtual ground"?)
Do you understand that, in an op amp, input current≈0? (This is important.)
If you assume the comparator output swings rail-to-rail (±10V), then I(Ri)=I(C)=±10V/10k=±1mA.
Since you want F=20kHz, and T=1/F=50usec, then T/2=25usec.
A capacitor charging at a constant current charges at the rate dv/dt=I/C, or C=It/V. We know that we want the cap to go from -5V to +5V in 25usec, so C=1mA*25usec/10V. Therefore C=2.5nF.
The comparator will switch each time its input voltage reaches zero volts. When the comparator output is +10V, V1 is going negative. When it reaches -5V, the comparator input must be zero volts. Therefore, R2/R1=2.