- #1

- 380

- 7

## Homework Statement

Let ##f:[-1,5]→ℝ## such that ##f(x)= \left\{

\begin{array}{l}

3, -1≤x<0 \\

0 , 0≤x≤2 \\

-2, 2<x≤5

\end{array}

\right. ##. Prove f is Riemann integrable.

3. The Attempt at a Solution

3. The Attempt at a Solution

Obviously f is bounded.

Let ##ε>0## arbitrarily.

Let partition of interval [-1,5] be P={-1,0,2,5}.

Then ##U(P,f)=3*(0-(-1))+0*(2-0)+(-2)*(5-2)=-3##

and ##L(P,f)=3*(0-(-1))+0*(2-0)+(-2)*(5-2)=-3##

Therefore ##U(P,f)-L(P,f)=0<ε##

Here comes the question: Is the partition I chose valid and correct?

Last edited: