Can these questions be solved above?

The midpoint rule is a recommended way to approximate a definite integral. In this question, we'll explore how accurate it is. Let's simplify our question so that we are tasked to approximate fo f(x)da so that f(x) is second order differentiable. This clearly ensures that f(x) is Riemann integrable. If we divide the interval [0, 1] into n segments and denote 2i - 1 C = i = 1, 2, . . . ,n, 2n then the midpoint approximation is S, = 1 21, f(x;). Define the error of the midpoint rule as En = \\Sn - (5.1) Our goal is to give upper bounds of E, in terms of n with the help of some other information. (a) If there exists A E R such that If' (x) |