A spring of stiffness ' \(k\) ' extended from a displacement \(x_{1}\) to a displacement \(x_{2}\). The work done by the spring is

(a) \(\frac{1}{2} k x_{1}^{2}-\frac{1}{2} k x_{2}^{2}\)

(b) \(\frac{1}{2} k\left(x_{1}-x_{2}\right)^{2}\)

(c) \(\frac{1}{2} k\left(x_{1}+x_{2}\right)^{2}\)

(d) \(k\left[\frac{x_{1}+x_{2}}{2}\right]^{2}\).