Help with calculus please

Question

For an object whose velocity in ft/sec is given by v(t) = -t² + 2, what is its displacement, in feet, on the interval t = 0 to t = 2 secs?

Options:

1)	1.333
2)	2.438
3)	2.667
4)	-4

Answer 1

v=-t^2 + 2

displacement is the integral of velocity

or velocity is the derivative of displacement

s = integral of v = -t^3/3 +2t + a constant (the initial distance)

from t=0 to t=2, evaluate the integral with those limits

s= -(2)^3/3 + 2(2) - 0 = -8/3 +4 = -8/3 + 12/3 = 4/3 = 1.333 feet

= 1 1/3 feet = 1 foot 4 inches