Evaluate the Line Integral $\int _ { C } x e ^ { x ^ { 2 } } d x + y \sin y ^ { 2 } d y$

Multiple Choice

Evaluate the line integral $\int _ { C } x e ^ { x ^ { 2 } } d x + y \sin y ^ { 2 } d y$ along the triangular path consisting of the line segment from $( 0,0 )$ to $( 2,3 )$ followed by the line segment from $( 2,3 )$ to $( 1,0 )$ followed by the line segment from $( 1,0 )$ to $( 0,0 )$ .

A) $0$
B) $\frac { 25 } { 9 }$
C) $\frac { 26 } { 9 }$
D) $3$
E) $- \frac { 8 } { 3 }$
F) $- \frac { 25 } { 9 }$
G) $- \frac { 26 } { 9 }$
H) $- 3$