Answer
$$
\int_{0}^{1} x^{2} \cos x d x
$$
Since
$$
0 \leq x \leq 1 \Rightarrow 0 \leq \cos x \leq 1 \Rightarrow x^{2} \cos x \leq x^{2}
$$
then we have :
$$
\int_{0}^{1} x^{2} \cos x d x \leq \int_{0}^{1} x^{2} d x=\frac{1}{3}\left[x^{3}\right]_{0}^{1}=\frac{1}{3}\left[x^{3}\right]_{0}^{1}=\frac{1}{3}[\text { Property } 7]
$$
Work Step by Step
$$
\int_{0}^{1} x^{2} \cos x d x
$$
Since
$$
0 \leq x \leq 1 \Rightarrow 0 \leq \cos x \leq 1 \Rightarrow x^{2} \cos x \leq x^{2}
$$
then we have:
$$
\int_{0}^{1} x^{2} \cos x d x \leq \int_{0}^{1} x^{2} d x=\frac{1}{3}\left[x^{3}\right]_{0}^{1}=\frac{1}{3}\left[x^{3}\right]_{0}^{1}=\frac{1}{3}[\text { Property } 7]
$$
