# It's about to hit the floor

Calculus Level 4

$\large\int_{-1}^{1}\{x^2+x-5\} \, dx$

If the value of the integral above is of the form $$\frac{1}{a}(b\sqrt{c}-d)$$ where $$a,b,c,d$$ are positive integers and $$b,c$$ are primes, find the value of $$a+b+c+d$$.

Note: $$\{x\}=\begin{cases}{x-\lfloor{x}\rfloor \quad , \quad x\geq0} \\ { x-\lceil{x}\rceil \quad , \quad x<0} \end{cases}$$.

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