How can you integrate this?

$\large I=\int _{ 0 }^{ 4 }{ \lceil x-1\rceil dx } =\sum _{ k=0 }^{ 3 }{ \int _{ k }^{ k+1 }{ \lceil x-1\rceil dx } }$

$\begin{matrix} I=\sum _{ k=0 }^{ 3 }{ \int _{ k }^{ k+1 }{ (k)dx } } & & \color{#3D99F6} \text { since } k-1\le x-1\le k \end{matrix}$

$I=\sum _{ k=0 }^{ 3 }{ k\left[ k+1-k \right] } =\sum _{ k=0 }^{ 3 }{ k } =0+1+2+3=6$