Some define the Dirac Delta Function as:
$$\int_{-\infty}^{\infty}\delta(x)f(x)\ dx=f(0)$$
For every continuous function $f$. In some books, I've noticed a different definition of $\delta(x)$ as an operation that satisfies the following two conditions:
$$\int_{-\infty}^{\infty}\delta(x)\ dx=1\quad\text{and}\quad\forall x\neq0:\delta(x)=0$$
Are the two definitions the same?