The process of approximating areas under curves led to the notion of a Riemann sum {{MATH_7}} where {{MATH_8}} is a nonnegative, continuous function on the interval {{MATH_9}}, and {{MATH_10}} is a sample point for the {{MATH_11}} rectangle, {{MATH_12}}. The limit of Riemann sums, as {{MATH_13}}, gives the exact area between the curve {{MATH_14}} and the interval on the {{MATH_15}}axis: {{MATH_16}} It does not matter whether we consider only right Riemann sums, or left Riemann sums, or midpoint Riemann sums, or others: the limit of any kind of Riemann sum as {{MATH_17}} is equal to the area, as long as {{MATH_18}} is nonnegative and continuous on {{MATH_19}}.