Evaluate:

Let

Now putting,

A(x+1)²+B(x+2)(x+1)+C(x+2)=x²+x+1

Now put x+1=0

Therefore, x=-1

A(0)+B(0)+C(-1+2) =1-1+1=1

C=1

Now put x+2=0

Therefore, x=-2

A(-2+1)²+B(0)+C(0) =4-2+1=3

A=3

Equating the coefficient of x²,A+B=1

3+B=1

B=-2

Form equation (1),we get,

So,