physics

Suppose we are given an arbitrary form for the acceleration a(t) of a particle that starts from rest at r(t_i)=0. What would be the derivation of its' position at r(t_f):

a)(t_f - t_i)⌠t_f a(t)dt
⌡t_i

b) v(t_f)+v(t_i)/2 ((t_f-t_i))

c)⌠t_f dt ⌠t dt'a(t') ???????
⌡t_i ⌡t_i

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