Exactly!!
Integrating is something that's really difficult with analog stuff, even if you take ultra precise parts. The reason is, that the integrator cap does collect any leakage currents (whether intrinsic input bias currents or caused by offset voltages) all the time. So, the error term gets bigger and bigger from alone...

With Prahlads application, at least 10000 samples for each mains' half period should be taken with a digital integrator though. Means, every 1µsec a sample had to be taken and had to be added to the integration sum. Should be doable?

Kai