Deriving potential energy

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Hello, i am trying to derive flexible energy, but i get a negative sign in front of a Work (A). Where did i miss?
F is force of a spring. I don't know if i used Hooke's law correctly...

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Thank you for looking.
 
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rcgldr
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I think you mean "elastic energy". And the elastic energy is a form of potential energy.
What you calculate is the work done by the elastic force between the points 1 and 2. This is equal to -(U2-U1).
 

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