Let the function \( f(x)=a x^{6}+b x^{5}+c x^{4}+d x^{3}+e x^{2}+f ...

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Let the function \( f(x)=a x^{6}+b x^{5}+c x^{4}+d x^{3}+e x^{2}+f x+g(a \neq 0) \) touches the line \( y=g(x)=x+p \) at \( x=1,2 \) and 3 , and \( h(x)=f(x)-g(x) \). If \( \int_{1}^{3} h(x) d x=\frac{32}{105} \), find the
\( \mathrm{P} \)
W value of \( a \).
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