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Consider the following problem:$\newline$The water level under a bridge is changing at a rate of $r(t)=40 \sin \left(\frac{\pi t}{6}\right)$ centimeters per hour (where $t$ is the time in hours). At time $t=3$, the water level is $91$ centimeters. By how much does the water level change during the $4^{\text {th }}$ hour?$\newline$Which expression can we use to solve the problem?$\newline$Choose $1$ answer:$\newline$(A) $\int_{3}^{4} r(t) d t$$\newline$(B) $\int_{0}^{4} r(t) d t$$\newline$(C) $\int_{4}^{5} r(t) d t$$\newline$(D) $\int_{4}^{4} r(t) d t$