Counter Example: If |f| is Riemann integrable, then f is not necessarily integrable

Question

I know that if |f| is Riemann integrable, then f is not necessarily integrable, but I am having difficulty in finding a counterexample. Could anyone help please?

Answer 1

$$ f(x)=\begin{cases}1&x\in\Bbb Q\\-1&x\notin\Bbb Q\end{cases}$$

Answer 2

For example when $f(x)=-1$ for all rational values of $x,$ and $f(x)=1$ for all irrational values of $x$ on $[0,1]$