Find the Work Done by the Force Field $\mathbf { F } ( x , y ) = ( x + y ) \mathbf { i } + x ^ { 2 } \mathbf { j }$

Multiple Choice

Find the work done by the force field $\mathbf { F } ( x , y ) = ( x + y ) \mathbf { i } + x ^ { 2 } \mathbf { j }$ on a particle that moves from the point $( 1,0 )$ to the point $( 2,2 )$ along the parabola $y = x ^ { 2 } - x$ .

A) $\frac { 15 } { 4 }$
B) $\frac { 15 } { 2 }$
C) $\frac { 49 } { 6 }$
D) $\frac { 49 } { 2 }$
E) $15$
F) $\frac { 15 } { 8 }$
G) $\frac { 49 } { 3 }$
H) $49$