Suppose that f : [a, b] R. a) If f is not bounded above on [a,

Question:

Suppose that f : [a, b] → R.
a) If f is not bounded above on [a, b], then given any partition P of [a, b] and M > 0, there exist tj ∈ [xj-1, xj] such that S(f, P, tj) > M.
b) If the Riemann sums of f converge to a finite number I(f), as ||P|| → 0, then f is bounded on [a, b].