Definite integral

Compare two definite integrals \( I_1=\int\limits_0^{\frac{\pi}2}\cos x\,\mathrm{d}x \) and \( I_2=\int\limits_0^{2\pi}2\cos x\,\mathrm{d}x \).

How much bigger is \( \int\limits_0^{\pi}(x+\sin x)\,\mathrm{d}x \) than \( \int\limits_1^{\pi}x\,\mathrm{d}x \)?

How many times is \( \int\limits_{\frac{\pi}6}^{\frac{\pi}3} \frac{\sin 2x}{\cos x}\,\mathrm{d}x \) bigger than \( \int\limits_{-\frac{\pi}3}^{-\frac{\pi}6} \frac{\sin 2x}{\sin x}\,\mathrm{d}x \)?

How much bigger is \( \int\limits_0^3\left[(x-3)^2+1\right]\!\mathrm{d}x \) than \( \int\limits_3^6 \log_55\,\mathrm{d}x \)?