\[ \mathbb{A} = \int_{0}^{1} 2x^3 \cos(x^2) \partial x + \int_{4}^{5} \dfrac{y+5}{y^2+y-2} \: \partial y \]

The above definite integral \( \mathbb{A} \) has a real value of \( \log\left ( \dfrac{a}{b} \right ) + \sin(c) + \cos(d) + f \), where \( a,b,c,d,f \) are integers and the fraction \( \dfrac{a}{b} \) is of simplest form.

Evaluate \( \displaystyle \int_{b}^{a} 6(cz^2+dz+f)\partial z \).

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