Integrators follow the basic time constant rules for Capacitors Ic=C dv/dt, T=RC, shown below re-arranged
(1) dv/dt= Ic/C or 5 V/1 s = Ic / 100 nF ... thus Ic = 500 nA = 0.5μA
or V/I=R = 5V/0.5μA = 10MΩ ( e.g. 10:1 scope probe)
(2) T = RC where T= decay of 60% = 1 second for your example from 5V on 100 nF cap
so R=T/C = 1 s /0.1 μF = 10MΩ
Ceramic and Electrolytic Caps have a self-leakage time constant on the order of magnitude of 1 second +/- 1 order of magnitude depending on vendor, and model
Plastic Film Caps have a self-leakage time constant on the order of 100 seconds to 1000 seconds and have lower density so tend to be much bigger and more expensive. Rank of quality and cost in descending order; Teflon, Polystyrene, Polyester,.
Anywhere a very high resistance is required, equally low input bias current Op Amps using FET inputs are needed. These requirements can be easily computed from basic formula given above.
To make an Integrate and Dump ADC converter, or Sample and Hold circuit , the prudent designer will also avoid using ceramic due to other non-linear behaviors like memory and voltage sensitivity. Plastic film is always the good choice.