How to calculate Area under Curve & FWHM using the computer program Origin?

Area under a curve can be estimated by integration method. (Check the references for more details.)

Full width at half maximum (FWHM) for a curve is used in many scientific data analyses. 
For instance, in X–ray diffraction (XRD) analysis of crystal data, it is used to find grain size.

 
It can be easily calculated using, quadratic equation. (Check the references for more details.)

This tutorial shows how to use the computer program Origin to estimate both 'Area under a Curve' as well as 'FWHM'.

Check these eNotes for  references
1. Full Width at Half Maximum (FWHM) & Quadratic equation
2. Introduction to Quadratic equation
3. Area under curve by integration method