Suppose that c 0 for x [c, d] and (x) = 0 elsewhere in [a, b], prove that R[a, b] and that

Suppose that c 0 for x ˆˆ [c, d] and φ(x) = 0 elsewhere in [a, b], prove that φ ˆˆ R[a, b] and that ˆ«Rb φ = a(d - c). [Given ε > 0 let δε := ε/4a and show that if a(d - c + 2δε).]