Answer
$F(x)=\frac{1}{4}x^4+x^2 -2x -4$
$F(2)=0$
$F(5)=\frac{669}{4}$
$F(8)=1068$
Work Step by Step
Find F(x) then evaluate at x=2,5,8
$\int^x_2 (t^3 +2t -2)dt$
$[\frac{1}{4}t^4 + t^2 -2t]^x_2$
$(\frac{1}{4}x^4 +x^2 -2x) -(4)$
$F(x)= \frac{1}{4}x^4 +x^2 -2x -4$
When x=2
$(4+4-4-4)=0$
When x=5
$(\frac{625}{4} + 25 -10-4)= \frac{669}{4}$
When x=8
$(1024 +64 -16-4)= 1068$
