Just to add to that (for GP, obviously): if "drawing" seems too abstract or calculating the area on the fly seems too hard, you can get similar intuition by gen

Just to add to that (for GP, obviously): if "drawing" seems too abstract or calculating the area on the fly seems too hard, you can get similar intuition by generating a wiggly/crinkly sequence (technical term) of numbers on your computer, then repeatedly take cumulative sums. This can even be done in excel (mash the number keys along a column for the initial function), and then you can graph the resulting sequences as functions. The cumulative sum is analogous to the integral, and the sequence will visibly get smoother. For the derivatives, take the difference repeatedly.