Cho $\int\limits_{1}^{3}{f\left( x \right)d\text{x}}=4$, khi đó...

Đặt $t=2\text{x}+1\Rightarrow dt=2\text{dx}\Leftrightarrow d\text{x}=\dfrac{dt}{2}$.
Đổi cận:

Ta có $\int\limits_{0}^{1}{f\left( 2\text{x}+1 \right)d\text{x}}=\int\limits_{1}^{3}{f\left( t \right).\dfrac{dt}{2}}=\dfrac{1}{2}\int\limits_{1}^{3}{f\left( x \right)d\text{x}}=2$.