SUMIFS using Fiscal Year Date Range

I'm trying to sum monetary amounts for a certain customer while referencing the data from a separate sheet. However, I only want to sum those amounts that fall within the FY20 (fiscal year) dates of 4/1/19 to 3/31/19.

Here's the start of my formula that sums all dates, but what conditional formula do I need to add that will only sum this specific date range?

Ex. =SUMIFS({COST1}, {Customer#}, "900264",.....?)

Thank you ~ Kate