Use a fiNite Sum to Estimate the Average Value of the Function

Use a finite sum to estimate the average value of the function on the given interval by partitioning the interval and
evaluating the function at the midpoints of the subintervals.
- $\mathrm { f } ( \mathrm { x } ) = 6 + \sin \pi \mathrm { x }$ on $[ 0,2 ]$ divided into 4 subintervals

A) $\frac { 24 + \sqrt { 2 } } { 4 }$
B) 0
C) 6
D) $\frac { 12 + \sqrt { 2 } } { 2 }$