Find $\int f(x)g(x) dx$ in $L^2$
$f(x) = \begin{cases} 1 & a<x<b \\ 0 & \text{otherwise} \end{cases}$ and $g(x) = \begin{cases} 1 & c<x<d \\ 0 & \text{otherwise} \end{cases}$
Note: $a<b<c<d$
I know the bounds on the integral of $f(x)$ are $b$ (upper bound) and $a$ (lower bound) and similar for $g(x)$, $d$ (upper) and $c$ (lower). However how can I calculate this integral?
Observe that, since $a<b<c<d$, one has $$ f(x)g(x) = \begin{cases} 0\color{red}{\,\,(=1\times 0)} & a<x<b \\ 0\color{red}{\,\,(=0\times 1)} & c<x<d \\ 0 & \text{otherwise} \end{cases} $$ giving $$ \int_{\mathbb{R}}f(x)\cdot g(x) \,dx =0. $$