Compute the line integral with respect to arc length of the function

f$($x$,$ y$,$ z$)=$ xy$2$

along the parametrized curve that is the line segment from

$(1,1,1)$

to

$(2,2,2)$

followed by the line segment from

$(2,2,2)$

to

$(3,6,5).(2,2,2)$ to $(-3,6,5).$