Work done = $\large\frac{1}{2} \times$ stress $\times$ strain $\times$ volume

$\qquad= \large\frac{1}{2}$$ \times Y \times (strain )^2 \times Volume $

$\qquad =\large\frac{1}{2}$$ \times Y \times \bigg( \large\frac{x}{L}\bigg)^2$$ \times AL$

$\qquad= \large\frac{Yx^2A}{2L}$

Hence b is the correct answer.

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