Let’s think of integration in a Riemann-like way: We have a function , and you take a particular interval of the variable , with , and split that interval into subintervals labelled by , each having width and (say) central value of , and then the integral $$\int_{[a,b]} f(x) \, \mathrm{d}x = \lim_{N \to \infty} \, \sum_{i=1}^N f(x_i) \, \Delta x .