The Solution $\mathbf { r } ( t )$ To the Differential Equation

Multiple Choice

The solution $\mathbf { r } ( t )$ to the differential equation $\mathbf { r } ^ { \prime } ( t ) = \sin t \mathbf { i } + \cos t \mathbf { j } + 3 \mathbf { k }$ with the condition $\mathbf { r } ( 0 ) = \mathbf { i } + \mathbf { j }$ is

A) $( \cos t + 2 ) \mathbf { i } - ( \sin t + 1 ) \mathbf { j } + 3 t \mathbf { k }$
B) $( - \cos t + 2 ) \mathbf { i } - ( \sin t + 1 ) \mathbf { j } + 3 t \mathbf { k }$
C) $( \cos t + 2 ) \mathbf { i } + ( \sin t + 1 ) \mathbf { j } + 3 t \mathbf { k }$
D) $( - \cos t + 2 ) \mathbf { i } + ( \sin t + 1 ) \mathbf { j } + 3 t \mathbf { k }$
E) $( \cos t + 2 ) \mathbf { i } + ( \sin t - 1 ) \mathbf { j } + 3 t \mathbf { k }$