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Could someone please help me with this problem?

## Homework Statement

A spring has a natural length of 20 cm. If a 25 N force is required to keep it stretched to a length of 30 cm, how much work is required to stretch it from 20 cm to 25 cm?

## Homework Equations

w=lim a to b f(x)dx

work=(force)(distance)

## The Attempt at a Solution

int. from 0 to 10 kxdx=25N

25=[1/2kx^2]0 to 10

25=1/2k(10)^2

25=50k

k=.5

int. from .05 to .10 (.5)xdx

Could someone please tell me if this is correct so far?

Thank you very much