How to use SUMIF to return sums between two values located in cells



I have two rows of data where I would like to use SUMIF to look at th
first row data (Row A) , and sum the values in the second row (Row B
if values are between those found in two cells (Rows C and D). I inten
to use the resulting bin values to compare different data sets, an
create a histogram like plots. There will be ~20,000 individua
output bins in the real data set, so doing it manually would b

Example Data

Row A, B:

A1= 1 , B1= 3
A2= 1.5, B2=3
A3= 2, B3 =5
A4= 2.2, B4 = 10
A5= 3, B4= 2

Row C, D, E

C1=0, D1=1, E1= SUMIF A between C1 and less than D1 then Sum B (ANS
C2=1, D2=2, E2= SUMIF A between C2 and less than D2 then Sum B (ANS
C3=2, D3=3, E3= SUMIF A between C3 and less than D3 then Sum B (ANS
C4=3, D4=4, E4= SUMIF A between C4 and less than D4 then Sum B (ANS
C5=4, D5=5, E5= SUMIF A between C5 and less than D5 then Sum B (ANS
C6=5, D6=6, E6= SUMIF A between C6 and less than D6 then Sum B (ANS

Thank you for any help you can provide


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