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Calculus Level pending

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 \(a +b+c\).

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