The work W needed to stretch/compress a spring from rest by a distance x is
W = 1/2 kx²
where k is the spring constant.
This means the work needed to change the length of this spring by 10 cm = 0.01 m is
W = 1/2 (200 N/m) (0.01 m)² = 0.01 J
and by 15 cm = 0.015 m is
W' = 1/2 (200 N/m) (0.015 m)² = 0.0225 J
Then the total work performed on the spring by stretching from 10 cm to 15 cm is
∆W = W' - W = 0.0225 J - 0.01 J = 0.0125 J
