Define $C(\alpha)$ to be the coefficient of $x^{1992}$ in the power series expansion about $x=0$ of $(1+x)^{\alpha}$. Evaluate  
$$  
\int_{0}^{1} C(-y-1)\left(\frac{1}{y+1}+\frac{1}{y+2}+\frac{1}{y+3}+\cdots+\frac{1}{y+1992}\right) d y.  
$$  

Let's think step by step and output the final answer within \boxed{}.
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