4.52 The number of integer solutions to the inequality $x-1<(x-1)^{2}<3 x+7$ 
(A) is equal to 4.
(B) is less than 4.
(C) is greater than 5.
(D) is equal to 5.
(China Junior High School Mathematics League, 1993)
［Solution］The given inequality can be transformed into
$$
\left\{\begin{array}{l}
x^{2}-3 x+2>0 \\
x^{2}-5 x-6<0
\end{array}\right.
$$
(1) The solution to the first inequality is $x<1$ or $x>2$;
(2) The solution to the second inequality is $-1<x<6$.

Thus, the integer solutions that satisfy the system of inequalities are only $x=0,3,4,5$ (see the figure above). Therefore, the answer is $(A)$.