Identify the correct relationship between unit step and unit impulse from the following.

Relationship $1$: ${\displaystyle \underset{0}{\overset{}{}}}(t)dt=u(t)$

Relationship $2$:$\frac{du(t)}{dx}=(t)$

Relationship $1$

Neither relationship$-1$ nor relationship$-2$

Relationship $2$

Relationships $1$ and $2$