`I_{4}`
`= int_{0}^{\frac{\pi}{4}} (2sin x + 3cos x)dx`
`= int_{0}^{\frac{\pi}{4}} 2sin xdx + int_{0}^{\dfrac{\pi}{4}} 3cos xdx`
`= -2cos x` $\mid_{0}^{\dfrac{\pi}{2}} + 3sin x \mid_{0}^{\dfrac{\pi}{2}}$
`= -2cos ((\pi)/2) + 2cos 0 + 3sin ((\pi)/2) - 3sin 0`
`= 5`
`I_{5} = int_{0}^{1} |2x - 1|dx`
`text{Xét dấu trong [0; 1], ta được}`
`I_{5}`
`= -int_{\dfrac{1}{2}}^{0} (2x - 1)dx + int_{1}^{\dfrac{1}{2}} (2x - 1)dx`
$= -(x^2 - x) \mid_{0}^{\dfrac{1}{2}} + (x^2 - x) \mid_{\dfrac{1}{2}}^{1}$
`= -(1/2)^{2} - 1/(2) + 0^2 - 0 + 1 - 1 - (1/2)^2 + 1/2`
`= 1/2`
