Evaluate the definite integral as limits of sums $\displaystyle\int\limits_a^bx\;dx$

Question

$\begin{array}{1 1}\large \frac{b^2-a^2}{2} \\ \large \frac{b^2+a^2}{2} \\ \large \frac{a^2-b^2}{2} \\ \large \frac{b^2-a^2}{4} \end{array} $