Riemann integrability of a piecewise function over $[1, 7]$ I have the following function 
$f(x) = \begin{cases} 2 & \text{if } 1 \leq x \leq 2, \\ 3 & \text{if } 2 < x \leq 4,\\ 1 & \text{if } 4 < x \leq 7. \end{cases}$
How do I determine if the function is Riemann integrable within $[1, 7]$? 
I think I have to check if the lower and upper integrals of $f(x)$ match but I’m unsure how to approach.  

hint
Let $\epsilon>0$ given and consider the partition $\sigma$ definef by
$$\Bigl(1,2-\frac{\epsilon}{7},2+\frac{\epsilon}{7} ,4-\frac{\epsilon}{7}, 4+\frac{\epsilon}{7},7\Bigr)$$
then
$$U(f,\sigma)-L(\sigma,f)=$$
$$(3-2)\frac{2\epsilon}{7}+(3-1)\frac{2\epsilon}{7}=\frac{6\epsilon}{7}<\epsilon$$
