If f is lebesque integrable  over [a,b] the f is Riemann integrable over [a,b] . The converse is also true.  true or false

Let f, g, h be functions on [a, b] such that f(x) ≤ g(x) ≤ h(r). Prove that if f and h are integrable with f f = fh, then g is integrable on [a, b] and So g = Sah.

Let f [a, b] → R be Riemann integrable and g: [a, b] → R be such that f(x) = g(x) for all xe (a, b). Prove that g is Riemann integrable and that b So = 1₁₁ 9- a

= Define ƒ : [0,2] → R by f(x) = 2x - r² for 0 < x < 1 and f(x) (x-2)² for 1 < x < 2. Prove that f is integrable on [0,2] and find the integral of f over [0,2]. Don not use Theorem 5.10, but rather find the integral by methods similar to those used in the proof of Theorem 5.8.