=SUBTOTAL(9,range)
If you want to sum only the visible rows in a filtered list (i.e. only those rows not filtered out), you can use the SUBTOTAL function. What makes SUBTOTAL especially useful is that it automatically ignores rows that are hidden in a filtered list or table.
Following the example in the screen above, to sum cells in column F for visible rows only, use:
=SUBTOTAL(9,D3:D7)
If you are hiding rows manually (i.e. right-click, Hide), use this version instead:
=SUBTOTAL(109,D3:D7)
The SUBTOTAL function can perform many other calculations, like COUNT, SUM, MAX, MIN, and more.