Integrate the Function F Over the Given Region $\mathrm { f } ( \mathrm { x } , \mathrm { y } ) = \frac { \mathrm { x } } { 6 } + \frac { \mathrm { y } } { 4 }$

Multiple Choice

Integrate the function f over the given region.
- $\mathrm { f } ( \mathrm { x } , \mathrm { y } ) = \frac { \mathrm { x } } { 6 } + \frac { \mathrm { y } } { 4 }$ over the trapezoidal region bounded by the $\mathrm { x }$ -axis, $\mathrm { y }$ -axis, line $\mathrm { x } = 6$ , and line $y = - \frac { 1 } { 2 } \mathrm { x } + 7$

A) $\frac { 209 } { 4 }$
B) $\frac { 321 } { 4 }$
C) $\frac { 153 } { 4 }$
D) $\frac { 125 } { 4 }$