What is the arc length of f(x)=x^2-3x+sqrtx on x in [1,4]?

${\int}_{a}^{b} \sqrt{1 + {\left(f ' \left(x\right)\right)}^{2}} \mathrm{dx} = {\int}_{1}^{4} \sqrt{1 + {\left(2 x - 3 + \frac{1}{2 \sqrt{x}}\right)}^{2}}$
$\approx 8.111$