Hookes Law and Spring Constant: Explaining the Integral

[Alec]

Hello, I'm having some problems with the spring constant "k" together with Hookes law. U=1\2kx^2

Could someone please explain how you get that integral?
If you insert it in a diagram and calculate the area as a triangle you would get 1/2kx. Where does the ^2 come from?

 

[arildno]

No, you don't!
Draw the triangle again.
How long is its base, and how long is its height?

 

[Alec]

Alright, my bad I missed that it's (kx * x)/2
Now, another question.
The function for F = kx.
The primitiv function for kx = (kx^2)/2 right? Because then you could calculate it as an integral?