$\lim_{\text{base}\rightarrow 0}\sum_{\text{rectangle}(a)}^{\text{rectangel}(n)}(\text{base})(\text{height})=\lim_{\Delta x\rightarrow 0}\sum_{i=1}^{n}\Delta x(f(a+\Delta xi))=\lim_{n\rightarrow \infty }\sum_{i=1}^{n}\frac{1}{n}f\left ( a+\frac{i}{n} \right )=\int_{a}^{b}f(x)dx$