Option C is correct answer.
Lim(x->0) on ( x^2 + x- Sin(x) ) / x^2
Solve the function first and then apply limit on every part of the function.
=( x^2 / x^2 ) + ( x / x^2 ) - ( Sin(x) / x^2 )
= 1 + 1/x - ( Sin(x) / x^2 ) ..........eq1
Apply limit on eq1
Lim(x->0) on 1 + Lim(x->0) on 1/x - Lim(x->0) on ( Sin(x) / x^2 )
=1 + Lim(x->0) on 1/x - Lim(x->0) on ( Sin(x) / x^2 )
(as we know Lim(x->0) on Sin(x) / x =1)
=1 + Lim(x->0) on 1/x - Lim(x->0) on 1/x
we get answer = 1