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 $( x , y , z ) = y z \mathbf { i } + x z \mathbf { j } + x y \mathbf { k }$ , and the curve $C$ is given by the vector function $\mathbf { r } ( t ) = t ^ { 2 } \mathbf { i } + t \mathbf { j } + t ^ { 3 } \mathbf { k } , 0 \leq t \leq 1$ .

A) $- 3$
B) $- 2$
C) $- 1$
D) $0$
E) $1$
F) $2$
G) $3$
H) $4$