Evaluate $\displaystyle \int^{\frac{\pi}{2}}_{0}2cosx+3sin2xdx + |\int^{\frac{5\pi}{6}}_{\frac{\pi}{2}}2cosx+3sin2x dx|$

The ans to this question is $\displaystyle 4.25units^2$ which is different from my answer of $\displaystyle 8.25units^2$

What I did

$\displaystyle \int^{\frac{\pi}{2}}_{0}2cosx+3sin2xdx + |\int^{\frac{5\pi}{6}}_{\frac{\pi}{2}}2cosx+3sin2x dx|$ $\displaystyle =$ $\displaystyle [2sinx-\frac{3}{2}cos2x]^{\frac{\pi}{2}}_{0}+|[2sinx-\frac{3}{2}cos2x]^{\frac{5\pi}{6}}_{\frac{\pi}{2}}|$

$\displaystyle =(3.5-(-1.5))+|(0.25-3.5)|$

$\displaystyle =8.25units^2$