# Sum of PDF HistogramList bar heights is 1/2, 1, 2, 3, etc... depending on distribution?

I've noticed that my normalized histograms are not always normalized to 1. For example:

tlist = RandomVariate[NormalDistribution[20, 5], 1000];
Histogram[tlist, Automatic, "PDF"]
dataList = HistogramList[tlist, Automatic, "PDF"];
pdfVal = dataList[[2]];
Total[pdfVal]


If you change the standard deviation of the NormalDistribution, you may see a change in the sum of pdfVal elements:

StdDev >>> Total[pdfVal]
1 >>> 2 or 5
2 >>> 2
3 >>> 1
4 >>> 1
5 >>> 0.5

I've noticed this with other histograms and other distributions as well (i.e. it is not specific to NormalDistribution).

Is there a way to force this to properly normalize to 1, or do I just have to do it by hand?

Plot[Total[