Answer
$n \geq 8$
Work Step by Step
The error bound for Simpson's Rule is given as follows: $|E_S| \leq \dfrac{M(b-a)^5}{180n^4}$
Now, the maximum value of $|f^{4}(x)|$ on $[1,2]$ is:
$M=3$
Further, $|E_S| \leq \dfrac{3 \times(2-1)^5}{180n^4}=\dfrac{1}{60n^4}$
we will choose $n$ such that $\dfrac{1}{60n^4} \leq 10^{-5}$
Therefore, $n \geq 6.4 \approx 7$
But as per Simpson's Rule, we need the even value of $n$ , thus $n \geq 8$
