Beach - Sandy Andy

a) R(t) is the rate at which sand is being removed by cubic yards/hour, so if you take the integral, it would give you the amount of sands by cubic yards (which the question is asking for )
eq: fnInt (2+5sin((4 pi t)/25), x, 0, 6) = about 31.816, so at t = 6, 31.816 cubic yards of sand has been removed

b) asking for amount of sand, so integral is needed,
fnInt(S(t)), x , 0, 6) - fnInt (R(t)), x, 0, 6) + 2500

c) asking for the rate, so no need to integrate, just plug in t=4
so... S(4) - R(4) = -1.909,
so at t = 4, the amount of sand is decreasing by 1.909 cubic yards/hour

d) Asking for amount of sand, so the graph of S(t) - R(t) would give you the slope, when the slope changes from - to +, you'll have a min,
at t= 5.1179 you have a minimum, that is where slope changes from - to + on the graph of S(t) - R(t) (slope graph)