**The question:**
An electrical signal S(t) has its amplitude |S(t)| tested (sampled) every 1/10 of a second. It is desired to estimate the energy over a period of half a second, given exactly by:

The result of the measurement are shown in the following table:

a) Using the above data for S(t), set up the appropriate Riemann sum and compute an appropriate value for the energy.

**My attempt:**
The set P (set of partitions) is clearly equal to {0, 1/10, 1/5, 3/10, 4/10, 1/2} so dt is 1/10 i.e. the width of each rectangle is 1/10.

My problem is with producing lower and higher Riemann sums. I'm used to having a function defined as something like

and producing a general sum given dx (in this case, dt). In this question, we don't know the function, we're just given values.

Does this mean I take the max/min of each interval (e.g. [0, 1/10], [1/10, 1/5] etc.) and work out the partitions by hand? I'm a bit confused.

Any help would be greatly appreciated!