there is a small error you add 1 to both sides but you did not do that for the middle

make into two inequalities then find the intersection for the two solutions

.....(1)

....(2)

(1)

you need to find the root of the polynomial to study the sign of x^3-x^2+x+2 and take the intervals of x values which make the inequality true but for this there is no exact root there is approximation root you can use intermediate value theorem or you write your question wrong

and for (2) it is same there is no exact root