Solution
= Solution
Only the $x$ component of the <vector field> is nonzero, so $\mathbf F\cdot d\mathbf r=(x^2+y^2)\,dx$. On the vertical segment, $dx=0$ throughout. Hence
$$
\boxed{\int_C\mathbf F\cdot d\mathbf r=0}.
$$
= Solution
Only the $x$ component of the <vector field> is nonzero, so $\mathbf F\cdot d\mathbf r=(x^2+y^2)\,dx$. On the vertical segment, $dx=0$ throughout. Hence
$$
\boxed{\int_C\mathbf F\cdot d\mathbf r=0}.
$$