Answer
$$ -\frac{1}{3} \cos (x^{3}+1)+C$$
Work Step by Step
Given
$$ \int x^{2} \sin \left(x^{3}+1\right)dx $$
Let
$$u=x^{3}+1\ \ \ \Rightarrow \ \ \ du= 3x^{2}dx$$
Then
\begin{aligned} \int x^{2} \sin \left(x^{3}+1\right) dx&=\frac{1}{3} \int \sin u d u \\ &=-\frac{1}{3} \cos u+C\\
&= -\frac{1}{3} \cos (x^{3}+1)+C \end{aligned}
