Have you considered breaking up the integral into analytic parts by partitioning it in the right way?
I've got a function
PV(t) = PV0 * (1 + ie)(D - t) * (1 - ii)(D - t)
which feeds into a step function, and which I have to integrate
F(t) = 0ID PV0 * (1 + ie)(D - [t]) * (1 - ii)(D - [t]) dt
(0ID...Integral; [t]...ceiling t)
To be perfectly frank and honest, I haven't got the slightest clue any more; you see, it's more than two decades now since I've been heavily engaged with mathematics...
...how could such a breaking up potentially be looking like?
As an example lets say we are integrating H(t-2) over the region 0 to 4 (H(t-a) is the Heaviside function where its 0 if t < a and 1 otherwise).
In this case you would break it up into two integrals: one with limits 0 to 2 and the other with limits 2 to 4 where the first integral would be 0dt and the other would be 1dt.
The basic idea is to make the integral analytic over the region so you can use the standard rules for that region.
Okay, so as long as I've got only a few interval steps to cover, it's kind of a piece of cake, but as the number of steps increases it appears to be rather a tedious undertaking, is it?
Considering the range t=0 to t=1,000,000 ideally I'd like to do F(1,000,000) - F(0) only...(I'm somehow more of the lazy persuasion!