* إذا it is given that::formula_10:where formula_11 is the supremum of "f" على formula_5, then "S" is defined to be an مجموع ريمان العُلوي.
* If it is given that::formula_12:where formula_13 is the supremum of "f" over formula_5, then "S" is defined to be an upper Riemann sum.