# Let's do some calculus! (9)

Calculus Level 4

$\displaystyle \lim_{x\to a}~{\dfrac{\displaystyle \int_{a}^{x}{f(x)} \,dx - \left(\dfrac{x-a}{2}\right)\left(f(x)+f(a)\right)}{{\left(x-a\right)}^{3}}} = 0$

For the above equation to be true, the maximum degree of $$f(x)$$ can be?