Dear Rich, thank you for your detailed answer, and I apologise for my scarce layout of an issue.
The purpose of the system is the low-noise acquisiton of low-frequency signals and this schematic is only the first part, ultra low noise amplifier. After that the signal is to be lead to ADC, and then through a transmitter and optical cable to a PC where the data is displayed and stored.
Batteries are indeed low noise. What I meant is that I need a stable DC voltage, so the varying voltage of the batteries doesn't affect the output. And by an integrator, I meant an op amp with a capacitor in the feedback loop (what I have been suggested to use). Thank you very much for your suggestion, perhaps it is a better option, since I don't know how to apply the 'JFET + integrator' solution anyways. Seems like a simpler solution as well. And please excuse my lack of experience and knowledge.