# What is the Formal Definition of the Definite Integral of the function y=f(x) over the interval [a,b] ?

${\int}_{a}^{b} f \left(x\right) \mathrm{dx} = {\lim}_{n \to \infty} {\sum}_{i = 1}^{n} f \left(a + i \Delta x\right) \Delta x$,
where $\Delta x = \frac{b - a}{n}$