Find the Value of the Line Integral $\int_{c}(4 x-3 y+1) d x-(3 x+y-5) d y$

Multiple Choice

Find the value of the line integral $\int_{c}(4 x-3 y+1) d x-(3 x+y-5) d y$ . (Hint: If $\mathbf { F } ( x , y ) = ( 4 x - 3 y + 1 ) \mathbf { i } - ( 3 x + y - 5 ) \mathbf { j }$ is conservative, the integration may be easier on an alternate path.)

A) $17 + 4 e - e ^ { 2 }$
B) $\frac { 1 } { 2 } \left( 17 + 4 e - e ^ { 2 } \right)$
C) $\frac { 1 } { 2 } \left( - 3 + 4 e - e ^ { 2 } \right)$
D) $\frac { 1 } { 2 } \left( 17 - 16 e - e ^ { 2 } \right)$
E) $- 3 + 4 e - e ^ { 2 }$