Recursive Integration

I integrated an integer $n$ with respect to a variable $x$ from $1$ to $n$ , and had a result of $c$ . I then integrated $c$ with respect again to $x$ from $1$ to $c$ and had a result of $c_2$ . Then I integrated $c_2$ with respect again to $x$ from $1$ to $c_2$ and had a result of $c_3$ . If $c_3 = n$ , and $n$ is a nonzero integer greater than 1, then the value of

$\huge \int^{n}_{1} nx^{n} dx$

can be expressed in the form $\frac {a}{b}$ where $a$ and $b$ are coprime positive integers. Determine $a+b$ .