Cho hàm số $y=f(x)=\begin{cases}x^2+3 &\text{khi }x\geq1\\ 5-x &\text{khi }x<1\end{cases}$. Tính $$I=2\displaystyle\int\limits_{0}^{\tfrac{\pi}{2}}f(\sin x)\cos x\mathrm{\,d}x+3\int\limits_{0}^{1}f(3-2x)\mathrm{\,d}x.$$
