There are 120 letters in a mailbox at 12:00 pm. Over the next 5 hours, the number of letters in the mailbox changes at a rate modeled by the function $r(t)$, where $r(t)$ is integrable and measured in letters per hour, and $t$ is the time in hours since 12:00 pm. Of the following statements, which one is the best interpretation of $\int _{ 0 }^{ 3 }{ { r(t)dt } } $?

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