Please help on this real analysis problem. The definition is attached also in case it's needed.

5. Let b > 0 and define f : [0, b] - R by f(x) = x. Prove that the lower Darboux integral for f on [0, b] is equal to , based on the definition.32.1 Definition. Let f be a bounded function on a closed interval [a, b]. For S C [a, b], we adopt the notationM(f, S) = sup{f(x) : xES} and m(f, S) = inf{f(x) : x ES}. A partition of [a, b] is any finite ordered subset P having the form P = {a = to M(f, [a, b]) . (th - th-1) = M(f, [a, b]) . (b - a); K =1 likewise L(f, P) 2 m(f, [a, b]) . (b - a), so m ( f, [a, b]) . (b - a)