Let `f(t)=|t-1|-|t|+|t+1|, AA t in R`. Find `g(x) = max {f(t):x+1letlex+2}, AA x in R`. Find `g(x)` and the area bounded by the curve `y=g(x)`, the X-axis and the lines `x=-3//2 and x=5`.

Answer

`g(x)={(-x-1,x <=-5//2),(4+x,-5//2 -1//2):}`
and area = `101/4` sq units.