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.