HPLC: peak area vs concentration

Many text books say that there is a proportionality between the peak area of the chromatogram and the concentration. However, in my opinion, there should be a proportionality between the concentration and the peak intensity, not the peak area. The peak intensity is increasing proportionally with respect to the absorbance of the substance. Hence, by using the Beer-Lamberant law, we can induce there is a proportionality between peak intenstiy and the concentration.

Is there any mathematical relation between the peak area and the concentration?

Any help will be appreciated.