The Fundamental Theorem of Calculus. Can someone help me understand this? I'm still not completely sure what i'm supposed to do.?

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a. s(t) = integral v(t) = -16t^2 + 16t + C <<< C = 32 feet .. initial height

s(t) = -16t^2 + 16t + 32

b. max height when s' = 0 which is when v(t) = 0

-32t + 16 = 0 ... t = 1/2

lands when s = 0 = -16t^2 + 16t + 32

t^2 - t - 2 = 0

(t-2)(t+1) = 0

t = 2 or t = -1 <<< time cannot be neg.

when t = 2 the balloon hits the ground

c. s(1/2) - s(0) = 4 ... distance balloon goes above the window where it is thrown upward

s(2) - s(1/2) = 32 ... dist. from window to the ground

s(2) - s(0) = 32 ... come on --- you can do something

d. 40 feet

e.... I can't do graphs on the comp. screen