What is s(t) if s'(t)=36t^5+4t^3?

According to the rule, s(t) could be determined evaluating
the indefinite integral of s'(t)

Int
(36t^5+4t^3)dt

We'll apply the additive property of
integrals:

Int (36t^5+4t^3)dt = Int (36 t^5)dt + Int (4
t^3)dt

We'll re-write the sum of integrals, taking out the
constants:

Int (36t^5+4t^3)dt = 36 Int t^5 dt + 4Int t^3
dt

Int (36t^5+4t^3)dt = 36*x^6/6 +
4*x^4/4

We'll simplify and we'll
get:

Int (36t^5+4t^3)dt = 6x^6 + x^4 +
C

The function  s(t)
is:  s(t) = 6x^6 + x^4 +
C