Happy days

Let $f(x)$ be a polynomial of degree three such that $f(0)=1, f(1)=2$ and $0$ is a critical point of $f$ having no local extreme. Find $\large \int_{ -1}^{1} \dfrac{f(x)}{\sqrt{x^2+7}} dx$ If the answer can be represented as $\large\ ln\frac{\sqrt{a} +1}{\sqrt{b} +c}$ the find the value of $a +b+c$ .