[tex]\int f'(x)dx=\int f'(x-1)dx\Rightarrow f(x)=f(x-1)+C[/tex]
Thay [tex]x=1\Rightarrow C=2018\Rightarrow f(x)=f(x-1)+2018[/tex]
[tex]\Leftrightarrow f(x)=f(x-1)-2018(x-1)+2018x\Leftrightarrow f(x)-2018x=f(x-1)-2018(x-1)[/tex]
[tex]\Rightarrow f(x)=2018x+C\Rightarrow f(0)=C\Rightarrow C=1\Rightarrow f(x)=2018x+1\Rightarrow \int_{0}^{1}(2018x+1)dx=[/tex]