Evaluate `int_(-1)^(2)|x^(3)-x|dx`

Explanation

clearly `f(x) = x^3-x = x(x-1)(x+1)`

we observe that

`f(x) gt0` for all x belong `(-1,0) cup (1,2)`

`f(x) lt 0` for all x belong `(0,1)`
Now ,
`int_-1^ 2|x^3-x|dx`

= `int_-1^0 (x^3-x)dx + int_0^1 -(x^3-x)dx + int_1^2 ( x^3-x)dx`

= `[x^4/(4)- x^2/2 ]_-1^0` + `[-(x^4)/(4)+ x^2/2 ]_0^1` + `[x^3- x ]_1^2`



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