When a rubber-band is stretched by a distance x ,it exerts a restoring force of magnitude $\;F=ax+bx^{2}\;$ where a and b are constants . The work done in stretching the unstretched rubber-band by L is :

Question

$(a)\;aL^{2}+bL^{3}\qquad(b)\;\large\frac{1}{2}(aL^{2}+bL^{3})\qquad(c)\;\large\frac{aL^{2}}{2}+\large\frac{bL^{3}}{3} \qquad(d)\;\large\frac{1}{2}(\large\frac{aL^{2}}{2}+\large\frac{bL^{3}}{3})$