Solution
= Solution
Parametrize the <straight line> by $\mathbf x(t)=(t,t,t)$, $0\leq t\leq1$. The <line integral> is
$$
\int\mathbf F\cdot d\mathbf x=\int_0^1\bigl[(2t^2+t)+(t^2+2t)+t\bigr]dt=\int_0^1(3t^2+4t)dt=\boxed{3}.
$$
The change in <scalar potential> is $\psi(1,1,1)-\psi(0,0,0)=-3$, so the answer is $-\Delta\psi$, as required by the <fundamental theorem for line integrals> for $\mathbf F=-\nabla\psi$.