When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude
F = ax + bx² where a and b are constants. The work done in stretching the unstretched rubber-band by L is :

• A

  ${\text{aL}}^2+{\text{bL}}^3$
• B

  $\frac{1}{2}\left({\text{aL}}^2+{\text{bL}}^3\right)$
• Correct answer
  C

  $\frac{{\text{aL}}^2}{2}+\frac{{\text{bL}}^3}{3}$
• D

  $\frac{1}{2}\left(\frac{{\text{aL}}^2}{2}+\frac{{\text{bL}}^3}{3}\right)$

Hence, the correct answer is option: 'C'.