In a book I am reading on special relativity, the infinitesimal line element is defined as $dl^2=\delta_{ij}dx^idx^j$ (Einstein summation convention) where $\delta_{ij}$ is the euclidean metric. Next, if we have some curve C between two points $P_1$ and $P_2$ in this space then the length of the curve is given as $\Delta L = \int_{P_1}^{P_2}dl$
I am having trouble deriving the next statement, which I quote:
A curve in D-dimensional Euclidean space can be described as a subspace of the D-dimensional spce where the D co-ordinates $x^i$ are given by single valued functions of some parameter $t$, in which case the length of the curve from $P_1=x(t_1)$ to $P_2=x(t_2)$ can be written $$\Delta L = \int_{t_1}^{t_2}\sqrt{\delta_{ij} \dot{x}^i \dot{x}^j} dt \qquad \mbox{where}\; \dot{x}^i\equiv \frac{dx^i}{dt}$$