`F = 16x`

We start compressing the spring at its natural length (0 m) and finish at 0.25 m from the natural length, so the lower limit of the integral is 0 and the upper limit is 0.25. So:

`"Work"=int_0^0.25 16x\ dx`

`=[8x^2]_0^0.25`

`=0.5\ text[N. m]`