Integration on $[0, \infty)$

Question

Let $\nu$ be a measure on $[0, \infty)$ and $c > 0$ be a constant. Why is it true that:

$$ \int\limits_{0}^{\infty} c^2 \left(\frac{1}{c} - \frac{1}{c + s}\right)\nu(ds) = \int\limits_{0}^{\infty} s^2 \left(\frac{1}{s} - \frac{1}{c + s}\right)\nu(ds) \quad ? $$

Answer 1

$$c^2\left(\frac{1}{c}-\frac{1}{s+c}\right)= \frac{c^2 \left(s+c-c\right)}{c(s+c)}= \frac{cs}{s+c}= \frac{s^2(c+s-s)}{s(c+s)}= s^2\left(\frac{1}{s}-\frac{1}{c+s}\right)$$