summation - Sum the series $(1^2+1)1! + (2^2+1)2! + (3^2+1)3! cdots + (n^2+1)n!$

Problem:

Sum the series:

$$(1^2+1)1! + (2^2+1)2! + (3^2+1)3! \cdots + (n^2+1)n!$$

Source: A book on algebra.I came across this interesting looking series and decided to tackle it.

My try :

All I have tried is taking the $r^{th}$ term and summing it, but in vain:

$$T_r = (r^2+1)r!$$
$$T_r = r^2\cdot r! + r!$$
Now I don't know how to sum either of these terms.I'm not familiar with uni level math as I'm a high school student. All help appreciated!