Answer
$$ L_4= 5.75,\ \ \ M_4= 7 $$
Work Step by Step
Since $n=4$, $\Delta x= \dfrac{b-a}{n}=\dfrac{4}{4}=1$ and $$x_0= 0,\ x_1= 1,\ x_2= 2,\ x_3=3,\ x_4= 4 $$ Then \begin{align*} L_{n}&=\left[f(x_0)+f(x_1)+.......+f(x_{n-1})\right]\Delta x\\ L_4&=\left[f(x_0)+f(x_1)+.......+f(x_{3})\right]\Delta x\\ &=\left[ f(0)+ f( 1)+ f(2)+f( 3) \right], \text{from the given figure }\\ &= \left[0.25+1+2.5+2 \right]\\ &=5.75 \end{align*} To find $M_4 $ \begin{align*} M_n&=\left[f\left(\frac{x_{0}+x_{1}}{2}\right)+\cdots+f\left(\frac{x_{n-1}+x_{n}}{2}\right)\right] \Delta x\\ M_4&= \left[f( 0.5)+f(1.5)+f(2.5)+f(3.5) \right], \text{from the given figure }\\ &= [ 0.5+2+2.25+2.25 ] \\ &=7 \end{align*}
