= Solution
{c}
<Green's theorem> for a positively oriented simple closed planar curve states
$$
\oint_C(P\,dx+Q\,dy)=\iint_D(Q_x-P_y)\,dx\,dy.
$$
Here $Q_x-P_y=1-(-1)=2$. The <trapezium> has parallel sides of lengths two and one, separated by height one, so its <area> is $3/2$. Therefore
$$
\boxed{\int_C\mathbf F\cdot d\mathbf r=2\cdot\frac32=3.}
$$
\b[Every congruent <trapezium> gives the same answer when its boundary is traversed anticlockwise], since the scalar <curl> is constant and <geometric congruence> preserves <area>. Reversing the traversal would instead reverse the sign.
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