Similar to Sean's fantastic response, mine also provides for a start and finish day. To choose the start and end days depending on E2 and E3, first, build two named ranges using Index/Match formulae as follows:
rngDay
=INDEX(Sheet1!$A:$A,MATCH(Sheet1!$E$2,Sheet1!$A:$A,0)):INDEX(Sheet1!$A:$A,MATCH(Sheet1!$E$3,Sheet1!$A:$A,0))
rngValue
=INDEX(Sheet1!$B:$B,MATCH(Sheet1!$E$2,Sheet1!$A:$A,0)):INDEX(Sheet1!$B:$B,MATCH(Sheet1!$E$3,Sheet1!$A:$A,0))
You can then click the series in the chart and modify the formula to:
=SERIES(Sheet1!$B$1,Sheet1!rngDay,Sheet1!rngValue,1)