Ok
Im not getting the same answer as my book
(1-t)(0,0,0) + t(0,0,1) = (0,0,t)
and (1-t)(0,1,1) + t(2,1,1) = (2t,1,1)
So for the first one
r' = (0,0,1)
F.r' = 0
So the integral of that is 0
Then for the second one
r' = (2,0,0)
F.r' = 4t + 8
so the integral between 1 and 0 = 10
But the answer in my book is 38/3