Prove Piecewise Function Integrable $$
f(x) =
\begin{cases}
-2, & \text{if }x < 0 \\
1, & \text{if }x > 0\\
0, & \text{if }x = 0
\end{cases}
$$
Hey guys I need some help showing that this function is integrable on the closed interval $[-1,2]$. 
So far my idea has been to show $$U(f,P)-L(f,P) < \epsilon$$ for some $\epsilon>0$.  
The only problem is the point $(0,0)$ on the function.  
I don't understand how to handle that.  
Can I just say that $U(f,P)$ for some partition will equal to $3$ and then find a partition $P$ for which $$3-L(f,P)<\epsilon?$$

Notice that for any $x$ at which $f$ is discontinuous, $x$ can be contained in an interval as small as you please. Make sure to include this small interval in your partition. 
