Question about integrals in physics

[WahooMan]

The equation that I have to find Impulse (J) is:

J = (integral from Ti to Tf) F * dt

I think dt means difference in time but I'm not sure. Can someone explain to me what dt is and how to calculate it?

[Fightfish]

dt refers to an infinitesimal small period of time, there is no 'calculation' of it. Basically, what the above integral is doing is summing up the change in momentum (impulse) at every instant in time, given by F dt, where dt is an infinitesimally small period of time during which the force F can be considered as constant.
To understand it better I recommend you look at a calculus text.

[superdave]

dt means you are integrating with respect to time. So t is the variable and everything else is a constant as far as integration goes.