# Happy days

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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