find an antiderivative F(x) with F'(x)=f(x) and F(0)=1

Question

f(x)=x^3+x

Answer 1

Int(x^3 + x)dx =
(x^4)/4 + (x^2)/2 + c
With x = 0, Int = 1 therefore c = 1
The complete antiderivative is:
(x^4)/4 + (x^2)/2 + 1
QED

Answer 2

ty!