Line integral Q: ellipse defined by r=cos(t) i+ sin(t) j +(2+sin(t)) k 0<= t<= 2pi

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Line integral Q: ellipse defined by r=cos(t) i+ sin(t) j +(2+sin(t)) k 0<= t<= 2pi

Hi, I just needed help checking my working.
I am trying to do a line integral with a vector space. Specifically, I have an ellipse in 3-space
defined by r=cos(t) i+ sin(t) j +(2+sin(t)) k 0<= t<= 2pi
with a vector field F=-y^2 i + x j + z^2 k
so I think I am correct in saying that I should integrate from 0 to 2pi
F . dr/dt
is that correct?
So my integrand is sin^3 t + cos^2 t +cos(t)*(4+4sin(t)+sin^2(t))
which, after a little work gives me pi

Thanks in advance for corrections, or a confidence boost.

best
s