Evaluate: `int_0^2[x^2-x+1]dx ,w h e r e[dot]` denotos the greatest integer function.

Explanation

Let first draw the graph of `y=x^(2)-x+1` for `0ltxlt2`

From the graph `(x^(2)-x+1)epsilon{((1//2,1),"if",0ltxlt1),((1,2),"if",1ltxlt(sqrt(5)+1)/2),((2,3),"if",(sqrt(5)+1)/2ltxlt2):}`
`:.int_(0)^(2)[x^(2)-x+1]dx=int_(0)^(1)0dx+int_(1)^(2)dx+int_((1+sqrt(5))/2)^(2) 2dx`
`=0((1+sqrt(5))/2-1)+2(2-(1+sqrt(5))/2)`
`=(5-sqrt(5))/2`