> The Number of Pieces an Integral is Cut Into

> You’re probably familiar with the idea that each piece has infinitesimal width, but what about the question of ‘how MANY pieces are there?’. The answer to that is a hypernatural number. Let’s call it N again.

Is that right? I thought there was an important theorem specifying that no matter the infinitesimal width of an integral slice, the total area will be in the neighborhood of (= infinitely close to) the same real number, which is the value of the integral. That's why we don't have to specify the value of dx when integrating over dx... right?