Evaluate the Line Integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$

Multiple Choice

Evaluate the line integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ , where F $( x , y ) = 2 x y \mathbf { i } + x ^ { 2 } \mathbf { j } + \mathbf { k }$ , and the curve $C$ is given by the vector function $r ( t ) = t ^ { 2 } \mathbf { i } + t ^ { 3 } \mathbf { j } + t \mathbf { k } , \quad 0 \leq t \leq 1$ .

A) $\frac { 1 } { 4 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 3 } { 4 }$
D) $1$
E) $\frac { 5 } { 4 }$
F) $\frac { 3 } { 2 }$
G) $\frac { 7 } { 4 }$
H) $2$