Help with anti derivatives

Question

Given,

f”(x)= 1x+0

and f’(0) = -5 and f(0) = -4

find f’(x) = ?

and find f(1) = ?

Answer 1

f"(x)= 1x + 0 = x

f'(x) = x^2/2 + C

f'(0) = -5 = (0)^2/2 + C = C

C =-5

f'(x) = x^2/2 -5

f(x) = x^3/6 -5x + K

f(0) = -4 = 0^3/6 -5(0) + K = K

K=-4

f(x) = (1/6)x^3 -5x -4

f(1) = 1/6 -5(1) -4 = 1/6-9 = -8 5/6

f(1) = -53/6