(

Mathematics -

Calculus)

Let f be a

bounded function defined on [a, b].

Let M(f, I) =

sup {f(x): x in interval I}.

Let P be a

finite partition such that P = {a =
t

_{0} <
t

_{1} <
t

_{2} < ...
t

_{n} = b}.

The upper Darboux sum, when written as U(f, P) is the

sum from k = 1 to n of
M(f,
[t

_{k-1},
t

_{k}])
|t

_{k} - t

_{k-1}|

*See also: Darboux integral.*