infinite Riemann sum

An infinite Riemann sum is a representation of an integral as the limit of the sum of areas of rectangles as $n$ (number of rectangles) approaches infinity.

LRAM (use the left $y$ value for the height of rectangle): ${\int }_a^{b}f(x)dx={\lim }_{n\to \infty }\frac{b-a}{n}\left[f\left(\frac{b-a}{n}\right)+f\left(\frac{2(b-a)}{n}\right)+f\left(\frac{3(b-a)}{n}\right)+\cdots +f\left(\frac{(n-1)(b-a)}{n}\right)\right]$

RRAM (use the right $y$ instead): ${\int }_a^{b}f(x)dx={\lim }_{n\to \infty }\frac{b-a}{n}\left[f\left(\frac{b-a}{n}\right)+f\left(\frac{2(b-a)}{n}\right)+f\left(\frac{3(b-a)}{n}\right)+\cdots +f\left(\frac{n(b-a)}{n}\right)\right]$