Chapter 4.4, Problem 10ES

To determine

The values of $f\left(-1\right),f\left(-0.5\right),f\left(0\right),f\left(0.5\right),f\left(1\right)$ such that the value of ${\displaystyle \underset{-1}{\overset{1}{\int }}f\left(x\right)}dx$ using the mid – point rule gives the value 12, composite trapezoidal rule with $n=2$ gives the value 5 and the Composite Simpson’s rule gives the value 6.