Use the Given Transformation to Evaluate the Integral $$\begin{array} { l } u = x + y , v = - 2 x + y ; \\\quad \int _ { R } \int _ { 2 } ( - 3 x + 4 y ) d x d y\end{array}$$

Multiple Choice

Use the given transformation to evaluate the integral.
- $$\begin{array} { l } u = x + y , v = - 2 x + y ; \\\quad \int _ { R } \int _ { 2 } ( - 3 x + 4 y ) d x d y\end{array}$$
where $R$ is the parallelogram bounded by the lines $y = - x + 1$ , $y = - x + 4 , y = 2 x + 2 , y = 2 x + 5$

A) $\frac { 29 } { 2 }$
B) 37
C) 29
D) $\frac { 37 } { 2 }$