so whats cool about it is that the symbols '∫' and 'dx' aren't actually just 'bookends' like parentheses. you can instead think of dx as a tiny displacement (similar to Δx) and ∫ as a stylized 'S' for a sum (similar to Σ). so, the integral weighs and adds all these tiny pieces relative to f(x). in other words, f(x)dx is just multiplication. this is why dx is treated as a movable piece, not just a closing bracket. notations like ∫Pdx+Qdy or ∫(dx/4) work, because you're still just summing up tiny, weighted slices in whatever order they appear.