Answer
a) the area is equal to L
b) the area is equal to U
c) the area is equal to U-L
Work Step by Step
a) We can see that the area $A$ of the shaded region in the first part becomes$\Sigma_{i=1}^n \triangle x_i \cdot m_i $ equal to lower bound $L$.
b) We can see that the area $A$ of the shaded region in the 2nd part becomes$\Sigma_{i=1}^n \triangle x_i \cdot M_i $ equal to upper bound $U$.
c) We can see that the area $A$ of the shaded region in the 3rd part becomes: $U-L=\Sigma_{i=1}^n \triangle x_i \cdot M_i-\Sigma_{i=1}^n \triangle x_i \cdot m_i $
