It has been given that $x$ is a real number and $m$ is an integer.
if $x$ is a real number then the number can be represented as $y.z$ where $y$ is the integral part and $z$ is the fractional part.
$\lceil \ x+m \ \rceil = \lceil \ (y+m).z \ \rceil = y+m+1$
and , $\lceil \ x \ \rceil +m = \lceil \ y.z \ \rceil+m = y+1+m$.
Thus both give the same result.