Physics derivation problem (see comment)

Question

anonymous · Answer

$$f(t)=(dp)/(dt) \rightarrow dp = f(t) dt \rightarrow \int\limits_{p1}^{p2} dp = \int\limits_{t1}^{t2} f(t) dt$$
I don't understand the third equation, with the integrals.  Usually when you integrate you have something like f=3x^2 and you integrate both sides with respect to a varable (in this case x) like so: $$\int\limits_{?}^{?} f dx = \int\limits_{?}^{?} 3x^2 dx = x^3 + c$$.  

In this example, we had a function that took a variable x, and derived it with respect to x.  In the equation above, we had dp (which may or may not be a function, i dunno) and f(t)dt just stuck an integral next to them.  

What functions are we integrating with respect to what variable?

anonymous · Answer

*took a variable x, and integrated it

anonymous · Answer

*stuck an integral sign