Let’s think of integration in a Riemann-like way: We have a function $f(x)$, and you take a particular interval $[a,b]$ of the variable $x$, with $a<b$, and split that interval into $N$ subintervals labelled by $i$, each having width $\Delta x = (b-a)/N$ and (say) central $x$ value of $x_i$, 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 .