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Consider the following problem:$\newline$The number of people remaining in the auditorium is decreasing at a rate of $r(t)=-0.1^{t}$ people per minute (where $t$ is the time in minutes). At time $t=1$, there were $75$ people remaining in the auditorium. How many people left the auditorium between minutes $1$ and $5$ ?$\newline$Which expression can we use to solve the problem?$\newline$Choose $1$ answer:$\newline$(A) $75+\int_{1}^{5} r(t) d t$$\newline$(B) $\int_{1}^{5}-r(t) d t$$\newline$(C) $75-\int_{1}^{5} r(t) d t$$\newline$(D) $\int r(t) d t$