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 ) $\frac{1}{2} (\frac{aL^2}{2} + \frac{bL^3}{3})$
( B ) $\frac{aL^2}{2} + \frac{bL^3}{3}$
( C ) $aL^2 + bL^3$
( D ) $\frac{1}{2} (\frac{aL^2}{2} + \frac{bL^3}{3})$