If the function is continuous and non negative over the interval ,

then the limits as of its lower sum and upper sum both

exist and are equal.

Apply formula for limits of the lower and upper sums:

The function is continuous and non negative over the interval ,

then the limits as of its lower sum and upper sum both exist

and are equal.

,

Where .

is minimum value of function on the subinterval.

is maximum value of function on the subinterval.

The statement is true.

The statement is true.