Solutions

a) $f(x)=-\cos x + c$ for $c\in\mathbb{R}$.

b)

$$f(x)=\frac{x^5}{20}+cx^2+dx+e$$

for $c,d,e\in\mathbb{R}$.

c)

$$f(x)=\frac{x^4}{24}+\frac{x^5}{120}+cx^3+dx^2+ex+f$$

for $c,d,e,f\in\mathbb{R}$.