− Let f : I → R, where I ⊆ R is an interval, be a mapping differentiable in the interiorI◦of I, and let a, b ∈ I◦with a < b. If |f0(x)| ≤ M for all x ∈ [a, b], then the following inequalityholds:¯ ¯ ¯f (x) −¯ ¯ b − a Z b a f (t)dt¯≤ M (b − a)¯ ¯ ¯ ¯ " + ¡ x −a+b(b − a)2¢2# (1)