An operational amplifier (op-amp) integrator is a circuit that performs the mathematical operation of integration on the input signal. It is essential to convert an ideal integrator into a practical integrator to avoid low-frequency saturation. Let's explore how this is achieved and why a resistor is added in parallel with the feedback capacitor:

1. In an ideal op-amp integrator, a capacitor is placed in the feedback loop of the op-amp. The voltage across the capacitor changes linearly over time in response to a DC input, leading to continuous integration.
2. The problem with this setup is that at very low frequencies, slight offsets or noise can cause the output to drift towards the supply rails, leading to saturation. This is because the DC gain in an ideal integrator is extremely high.
3. To counteract this issue, a resistor is typically added in parallel with the feedback capacitor. This modifies the frequency response of the integrator such that:
   • At low frequencies, the resistor dominates the feedback path, and the circuit behaves like an amplifier with finite gain to prevent saturation.
   • At higher frequencies, the capacitor still acts to integrate the input signal.
4. This practical approach ensures the circuit is stable and avoids drift or saturation at low frequencies without significantly affecting the integration performance at higher frequencies.

Thus, the correct component to be added is a resistor in parallel with the feedback capacitor, which helps maintain the stability and functionality of the circuit across a range of frequencies.

In conclusion, the correct answer is A resistor, which prevents low-frequency saturation effectively by limiting the DC gain of the integrator.