To find the area between the curves, you need to figure out which function has higher $y$ values to pick as $f(x).$ Caution, the functions could be such that they switch which function has higher $y$ values for different $x$ values. $($See figure$).$ Notice $f(x)>g(x)$ when $g(x)>f(x)=A1+A2g(x)f(x)0.$ You would find the area for each part and add the areas together. Total area $=A1+A2.$

$g(x)$

$A2$

$f(x)$

$A1-1,$ and $g(x)>f(x)$ when $0.$ You would find the area for each part and add the areas together. Total area $=A1+A2.$

$g(x)$

$A2$

$f(x)$

$A1$