Riemann integrals

c) Below is an alternative but equivalent definition of the definite integral of f: R - R between a and b , given xx = a + k (,# ) for Oksn: In(f,a, b) = b - a K=0 [f(x)dx = lim In (f, a,b) i) For f(x) = x2 , calculate Is(f,-2,8) . Show your working. ii) We now define In(f, a, b) = K=1 For f(x) = x2 , calculate Js(f, -2,8). Show your working. iii) Calculate , x2dx iv) We call a function f: R - R monotone increasing if x> y implies f(x) > f(y). Show that, if f is monotone increasing, then, for any a, be R, a