How in the world did you try integrate that?

If f(x) = x^5 + 5*sqrt(x) = x^5 + 5*x^(1/2), then

F(x) = (x^6)/6 + (5*x^(3/2))/(3/2) = (x^6)/6 + (10x^(3/2))/3 + C

We are given F(1) = -4; thus,

-4 = 7/2 + C (we got this by plugging 1 in for all the x's above)

Solve for C:

C = -15/2.

Replace the C above with what you solved, and you have F(x).