let $f$ be a step function, f:\left[0,2\right]\longrightarrow\mathbb{R} , f\left(x\right)=\begin{cases} 1 & 0\leq x<1\\ 3 & x=1\\ 2 & 1
intgerate ${\displaystyle \intop_0^2 f\left(x\right)\,dx}$ using the $U\left(f,P\right),L\left(f,P\right)$ definition.