Answer to Question #63167 in Real Analysis for nik

Question

(a) Let a, b ∈ R with a < b. Define f : [a, b] → R by
f(x) = (
b if x = a,
a if a < x ≤ b.
Use the definition of the Riemann integral to prove that f is integrable on [a, b] and
determine the value of the integral R b
a
f