Verified answer

We define an antiderivative as F(x) = integral(t=a to x)(f(t) dt).

Now f(x) >= 0 for x < 1, so to have F(1) = 0 we must have a = 1.

So F(5) = integral(t=1 to 5)(f(t) dt) =

[(10/3)*t^3 - (7/6)*t^6] (from t = 1 to t = 5) =

[(10/3)*5^3 - (7/6)*5^6] - [(10/3) - (7/6)] = -106888/6 = -53444/3.