Answer
$\textbf{True}$
Work Step by Step
(See Theorem 4.3)
The limits as of both the lower and upper sums exist and are equal to each othe and to the definite integral between a and b.
$$\lim\limits_{n \to \infty}s(n) = \lim\limits_{n \to \infty}S(n) = \int_a^b f(x)dx$$
