calculus, function, f(x) help

Question

Consider the function f(x)=x^4+7(x^1/2)

let F(x) be the antiderivative of f(x) with F(1)=-6

Then F(x)=

Answer 1

Why don't you use the Power Rule to integrate f(x) and then set x=1 to determine the constant of integration?

For example, if f(x) was x⁵ + 4x^(1/2) then the integral would be

F(x) = x⁶/6 + 8x^(3/2)/ 3 + C

and using the condition F(1) = -6 gives

1 + 8/3 + C = -6 ==> C = -36/6 - 17/6 = -53/6, so

F(x) = x⁶/6 + 8x^(3/2)/ 3 - 53/6