Dear Kumar,
As per you mentioned you are having variable in spatial domain only i.e. my_variable(lat, lon) is it ? If it is so then you have to simply use the @din transformation to compute the integration. over the area.
let integrare_variable = my_variable[x=@din, y=@din]
this will results you into a single numeric value over the defined area.
moreover if you have 360*180 domain and you want to integrate only the indian ocean then just use my_variable[x=20:120@din, y=-30:30@din]. same thing you can apply to depth variable as well. So you can integrate along any dimension, depending on your requirement.
this is the definite integral and will integrate only the point of actual data not the fill and NaN values grid e.g. Land.
let us know if you have any other query.