For a continuous function $f,we$ approximated ${\displaystyle \underset{a}{\overset{b}{}}}f(x)dxby$ two

ways. The first $is$ the trapezoidal rule with $n=1,$ where the second $is$

the Simpson's rule with $n=2.If$ the two method gave the same

result, then $f(\frac{a+b}{2})=$

Select one:

$a.\frac{f(a)+f(b)}{3}$

$b.\frac{f(a)-f(b)}{2}$

$C.\frac{f(a)+f(b)}{2}$

$d.\frac{f(a)+f(b)}{4}$