My calculus is a bit rusty, but you know that.
I have a summation in mind that I want to express as an integration. The summation: we divide the time between now and expiry into equal parts delta t. We want to sum the sensitivity to change of time (theta) at each point in time and multiply by delta t to give a time decay. The corresponding integral is trivial. We also want, assuming that the price F is a function of t, to sum the sensitivity to price at each point in time, and multiply by the change in price delta F, to get the total P/L corresponding to change in price. The summation is trivial, but how do we express the integral? I would multiply by dF, but dF is not the variable of integration here.