Is the following function riemann integrable? Is the following function Riemann integrable on [-5,5] and if so, what is the value of; 
$$
\int_{0}^5 f(x)\;dx
$$
$$
f(x) = \left\{\begin{aligned}
&1 &&: |x| \ge 1\\
&0 &&: Otherwise
\end{aligned}
\right.$$
Must I prove this is Riemann integrable by finding L and U and comparing? Im lost with what must seem like a trivial problem any help greatly appreciated.

$$f(x)=\chi_{[1,5]}(x)+\chi_{[-5,-1]}(x)$$that's the sum of integrable functions.
To compute the integral:$$\int_0^1f(x)=\int_0^10=0$$$$\int_1^5f(x)=\int_1^51=4$$ and therefore$$\int_0^5f(x)=4$$
