Water is being pumped out of a storage tank at a rate of $R(t)=10\sqrt{\cfrac{2t}{t+2}}$ cubic feet per minute, where $t$ is measured in minutes. The tank is full at time $t=$0 containing $100$ cubic feet of water.

How much water is pumped out of the tank from time $t = $1 to time $t = 5$ minutes?

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