You can either compute three line integrals, or use Stokes' theorem and compute one surface integral. I prefer the latter.
The curl of the given vector field is
Parameterize the triangular surface bounded by
- I'll call it 
- by
with
and 
. By Stokes' theorem, we have
where is positively oriented; that is, every vector normal to is pointed in the positive 
direction. The surface element is given by
So our integral is
The curl of the given vector field is
Parameterize the triangular surface bounded by
with
where
So our integral is
