Alternating signs

Calculus Level 5

$\displaystyle y= \sqrt{x-\sqrt{x+\sqrt{x-\sqrt{x+\sqrt{\cdots}}}}}$

Given that $\displaystyle \int_{1.75}^{4.75} y \,dx = \frac{a}{b}$ , where $a$ and $b$ are coprime positive integers, find $a+b$ .