$\mathbf { r } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j } , 0 \leq t \leq 2 \pi$

Multiple Choice

$\text { Evaluate } \int _ { C _ { 1 } } y ^ { 3 } d x + \left( 27 x - x ^ { 3 } \right) d y \text {, where } C _ { 1 } \text { is the unit circle given by }$
$\mathbf { r } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j } , 0 \leq t \leq 2 \pi$

A) $\frac { 51 \pi } { 2 }$
B) $\frac { 49 \pi } { 2 }$
C) $\frac { 57 \pi } { 2 }$
D) $\frac { 27 \pi } { 2 }$
E) $\frac { 59 \pi } { 2 }$