All real-world circuits have some DC offsets, and a pure integrator has infinite DC gain. The result is that a pure integrator will inevitably drift over time.
That drift can be managed in various ways.
- The integrator may be included in a larger feedback loop, which corrects for the drift.
- The integrator may be designed with a "reset" function which is triggered periodically.
- The integrator may be made deliberately impure.
The resistor makes the integrator impure. At low frequencies it behaves like a regular amplifier with a gain set by the resistors, at high frequencies it behaves like an integrator.
The value of the resistor is a compromise, a smaller resistor will result in less DC offset in the output, but at the price of more distortion of the slope.
I don't know where the author of your book got their "10R" figure from. If I have to guess I would say that they probably assumed that the circuit would be operated in a configuration where the input and output voltages were roughly the same and then made some assumption about what level of error was acceptable.