I am supposed to find the upper Darboux sum of a function $f$, where:
Let $D$ be a partition of the interval $$\left [ 0,1 \right ] $$ in five intervals of equal length and the function $f$ be $$ f(x)=kx,\text{ where }k<0. $$ What is the upper Darboux sum of $f$ respect to the partition $D$?
I know that the upper Darboux sum of $f$ with respect to $D$ is defined as: $$ U_{f,D}=\sum _{i=1}^{n}(x_{i}-x_{i-1})M(f,\left [ x_{i-1},x_{i} \right ]) $$ and I know that the length of my interval is 0.2, but I do not understand the part with supremum, or how exactly I should do it.