Answer
$$g'(s) = (s - s^2)^8$$
Work Step by Step
$$g(s) = \int\limits_5^s{(t - t^2)^8}dt$$
Plug upper bound into t and multiply by the derivative of the upper bound (chain rule).
$$g'(s) = ((s)-(s)^2)^8 \times (s)'$$
Simplify.
$$g'(s) = (s-s^2)^8$$