# Concern regarding infinitesimal errors

When finding out the area under a curve,we divide it into many thin strips and them sum up.My question is when we write for example $$dW=F×ds$$ and then integrate in physics terminology,we are referring to a width of $$ds$$ and a height of $$F$$.But in a curve we cannot find a perfect rectangle because the two heights won't be the same,though they will be close but not exact.If calculus is the measure of precision,why can we then write $$dW=F×ds$$ while we know the area of the small region will not exactly be the area of the rectangle and there will be some errors.So when we add all the infinitely thin rectangles,won't there be a small error since we are actually leaving space?I mean even when we have infinitely small width,it still isn't a perfect rectangle. P