Hello, I don't know if this is a "Calculus" question or not but it was brought up in Calculus 2 and I didn't quite understand.

If f(t) is measured in pounds and x is measured in feet, what are the units of

integral(a to b) f(t)dt.

From what my teacher explained, the new units would be Foot-pounds?

I just don't understand how this works. It seems like non-sense to me and I felt like some how along the way I missed something critical about units.

Can someone explain it to me?

Thank you