smc

Notice that $\text{[}x\text{]}$ is just $\lfloor x\rfloor$. We see that $\text{I}$ is true, as adding by one does not change the fraction part of the number. Similarly, $\text{II}$ is false, because $\text{[}x+y\text{]}$ does not always equal $\text{[}x\text{]}+\text{[}y\text{]}$ (If both numbers were $1.5$, $\text{[}1.5+1.5\text{]}=3$, $\text{[}1.5\text{]}+\text{[}1.5\text{]}=2$). Because $\text{I}$ is true and $\text{II}$ is false, the answer is $\boxed{\text{I }\text{only}}$.