Quote by douglis
he described the "total/overall force" as the effect of force over time so the ∫f(t)dt is exactly what he means.

Ah, ok. That is a defined term in physics, called impulse:
http://en.wikipedia.org/wiki/Impulse_(physics)
Edit: I see sophiecentaur already mentioned it.
I just want to point out that impulse does not have units of force, it has units of momentum. Assuming that we are talking about the impulse over one full rep then the change in momentum is 0 so the impulse on the weight is 0.
The only two forces acting on the weight are gravity and the human, so the impulse provided by the human is equal and opposite to the impulse provided by gravity. So, the impulse is equal to the weight times the duration of the rep. Therefore the human provides a larger impulse on a slow rep than on a fast rep.
waynekx8, if by "total force" you mean "impulse" then it is greater for a slow rep than for a fast rep. If you mean some other quantity then please define it explicitly.