Let $F(t)=\frac{t^2-3t-4}{t+1}i+\frac{t+2}{t-4}j+\frac{(t+1{)}^2}{sin(t+1)}k,$ find $\underset{t-1}{lim}F(t).$

$A.($:$3,\frac{1}{-5},1$:$)$

$B.($:$-5,\frac{1}{-5},0$:$)$

$C.$ Does not exist

$D.($:$-5,\frac{1}{-5},1$:$)$

$E.($:$\frac{0}{0},\frac{1}{-5},\frac{0}{0}$:$)$