you amplify by AC coupling before the integrator the offset in the integrator will be a much smaller percentage of the signal than if you do not.

Thanks erik for your quick helpfull responses,

Even that small percentage will accumulate and will become a huge error. Since I will continously integrate for hours. I think the only way to do it properly is using a Chopper stabilized auto zero Op-Amp for integration purpose. And of course the AC coupling to get rid of DC component coming along with AC signal.

Thanks & Regards,
Prahlad Purohit