Riemann Sum on a Tagged Partition

Let $a,b\in\mathbb{R}$ with $a<b$, let $f:[a,b]\to\mathbb{R}$, let $P=(x_0,x_1,\dots,x_n)$ be a partition of $[a,b]$, and let $(t_1,\dots,t_n)$ determine a tagged partition of $[a,b]$ relative to $P$. The corresponding Riemann sum of $f$ is the real number $\sum_{i=1}^n f(t_i)(x_i-x_{i-1}).$