Question

Let f : [a,b]→R be a bounded function on a closed interval [a,b], let P = {x₀ ,x₁ ,…,xₙ} be a partition of [a,b], and let d be a real number such that f(x) ≤ d for all x∈ [a,b].
(a). Given any i ∈{1,2,…,n}, show that ℓᵢ ≤ uᵢ ≤ d, with the