Exercise 5.2.2: Let f and g be in R[a;b]. Prove, without using Proposition 5.2.5 , that f +g is in R[a;b] and Z b a f (x)+g(x) dx = Z b a f (x) dx+ Z b a g(x) dx: Hint: One way to do it is to use Proposition 5.1.7 to find a single partition P such that U(P; f )L(P; f ) < e=2 and U(P;g)L(P;g) < e=2.