Given that
F(0) = 3, which gives,
3 = 0 – 6 × 0 + C    or    C = 3
Hence, the required anti derivative is the unique function F defined by
F(x) = x4 – 6x + 3 Remarks
(i)
We see that if F is an anti derivative of f, then so is F + C, where C is any
constant Thus, if we know one anti derivative F of a function f, we can write
down an infinite number of anti derivatives of f by adding any constant to F
expressed by F(x)  + C, C ∈ R In applications, it is often necessary to satisfy an
additional condition which then determines a specific value of C giving unique
anti derivative of the given function