If

is an integrable function in the interval

and if

is a primitive function of

in

then it verifies that

*Proof*
For any

partition of

by applyin' the MVT to

in each one of intervals

we can ensure that it does exist a point

(for each

) such that

Summing member to member the previous equalities, we get

Let

and

be the infimum and supremum of

in

and according to lower and upper sums

and

of

to the

partition, respectively, as one wants it

it yields

Hence,

is included between the lower and upper sums of

for any

partition, and this property has the integral

from here