hello,
could you please explain where did you model, like matlab or spice..? One reason could be there may be some max value on the o/p, which you are observing like saturation, generally integrators can't be run in open-loop..

Thanks,
raj.

NTR,
I'm guessing you don't have a pole at DC; I didn't try it, but I suspect you use H=1.257e010/(s + 6.283e007). This is a low pass, not an integrator.
- B O E

NTR,
sorry that my first answer was apparently not elaborate enough:
Of course, any practical (real) implementation of an integrator will be lossy, i.e. it will not have infinite DC gain. However, a gain of 200 or so is far from a good implementation for an integrator (i.e. it has significant non-idealities).
If the DC gain is large enough, saturation will be the limiting factor; however, your model (just the transfer function) does not include saturation, so you get the finite DC gain as limiting factor.
- B O E
[PS:] I called it a low-pass filter to highlight the non-idealities of the integrator.

NTR,
essentially this is a question of trade-off between effort and cost (area, power, ...) for building a better integrator vs. achieved/required performance of your system.
A (first-order) low-pass filter acts as an integrator over time intervals Δt ≪ τ, so you need to figure out over what time you have to integrate to achieve the performance you need.
- B O E