Sum range between two index-matched values from column

Hi I am trying in vain, to put together Index and Match formula which will sum values from range noted in Column H to Column H, depending on Values in I1 to L1 to table in Column A to E.

for example in I2 value should be 21 i.e sum of D2 to D4.

Any help much appreciated, thanks.

For I2 how about

Formula:

=SUMIFS(D:D,A:A,">="&G2,A:A,"<="&H2)

Thank you, works very well

One more variant:

PHP Code: 

Cell I2 = IFNA(SUM(INDEX($B$2:$E$7,MATCH($G2,$A$2:$A$7,0),MATCH(I$1,$B$1:$E$1,0)):INDEX($B$2:$E$7,MATCH($H2,$A$2:$A$7,0),MATCH(I$1,$B$1:$E$1,0))),"") 


Formula

=IFERROR(SUM(INDEX($B$2:$E$7;MATCH($G2;$A$2:$A$7;0);MATCH(I$1;$B$1:$E$1;0)):INDEX($B$2:$E$7;MATCH($H2;$A$2:$A$7;0);MATCH(I$1;$B$1:$E$1;0)));"")