Let $f : \mathbb { R } _ { \geq 0 } \longrightarrow \mathbb { R }$ be the function
$$f ( x ) = \begin{cases} 1 , & x = 0 \\ x ^ { - x } , & x > 0 \end{cases}$$
Determine whether the following statement is true:
$$\int _ { 0 } ^ { 1 } f ( x ) \mathrm { d } x = \sum _ { i = 0 } ^ { \infty } n ^ { - n }$$