0 if a lt;gt;lt;c

Let a, b, c, d E R such that a lt; c lt; d lt; b. Let f : [a, b] – R, f(x) :=

1 ifclt;xlt;d.

0 ifd lt;xlt;b

Prove that f is Riemann integrable on [a, b] and that

f =d-c.

Remark: The function f defined above is called an elementary step function.

Hint: Do not solve this question by directly applying the definition of Riemann integrability.

Instead, combine already known results on Riemann integrability.Math