Answer
The work required to stretch the spring is equal to the work required to compress the spring $x$ units from equilibrium.
Work Step by Step
The work required to stretch the spring can be found as:
$W=\int_0^x F(x) \ dx=\int_0^x 25 x \ dx\\=|\dfrac{25 x^2}{2}|_0^x\\=12.5 x^2$
Next, the work required to compress the spring can be found as:
$W=\int_0^{-x} F(x) \ dx=\int_0^{-x} 25 x \ dx\\=|\dfrac{25 x^2}{2}|_0^{-x}\\=12.5 x^2$
This implies that the work required to stretch the spring is equal to the work required to compress the spring $x$ units from equilibrium.
