Cho hàm số $f\left( x \right)$ liên tục trên $\mathbb{R}$ thỏa...

Ta có:
Từ đó có: $\left\{ \begin{aligned}
& F\left( 2 \right)=-2F\left( 1 \right)+C \\
& F\left( 4 \right)=-2F\left( 5 \right)+C \\
\end{aligned} \right.$$\Rightarrow F\left( 2 \right)-F\left( 4 \right)=2\left( F\left( 5 \right)-F\left( 1 \right) \right) \Rightarrow F\left( 5 \right)-F\left( 1 \right)=12\int\limits_{1}^{5}{f\left( x \right)\text{d}x}=\left. F\left( x \right) \right|_{1}^{5}=F\left( 5 \right)-F\left( 1 \right)=12$.