Show there does not exist a continuously differentiable function $f$ on $[0,2]$ such that $f(0)=-1$, $f(2)=4$ and $f'(x)\le2$ for $0\le x\le2$ [closed]

Show there does not exist a continuously differentiable function $f$ on $[0,2]$ such that $f(0)=-1$, $f(2)=4$ and $f'(x)\le2$ for $0\le x\le2$.

I am not sure how show this is the case using the fundamental theorem.

I know the formula for the fundamental theorem of calculus:so for this problem integral from $0$ to $2$ of $f$ is $5$.