Evaluate $I=\int_{\mathcal{C}} (\sin x + 6 y)\,dx+(3 x+y)\,dy$ for the nonclosed path $ABCD$ in the figure.

$A=\left(0,0\right),\quad B=\left(1,1\right),\quad C=\left(1,2\right),\quad D=\left(0,3\right)$

$I=$