Hey, I'm a math novice. As far as I can tell, we use integrals to solve such problems as the area beneath a curve. If I understand it correctly, integrals use a method where an infinite series of rectangular columns are shot up at the curve to probe its varying slope. These columns, because they are flat on top, have their corners sliced off by the varying curved slope, and integrals are designed to sum and cancel all these extra sliced off column shavings, so that we get a true picture of the varying slope. If this is wrong already, please correct me. So I was wondering, are integrals perfect at finding the area beneath a curved slope, or are they approximations? Thanks.