The help page says that an option for int is continuous=truefalse. The help page reads

"Specifies whether int looks for discontinuities. " I interpret that as continuous=true means look for discontinuities

and false means do not look. A simple example, however, suggests that it is the opposite.

int(3/(5-4*cos(x)),x=0..2*Pi,continuous=true)=0

int(3/(5-4*cos(x)),x=0..2*Pi,continuous=false)=2*Pi.

I interpret this as continuous=true means "I guarantee the result is continuous, so do not look"

This would be a logical opposite to discont=true in the plot command: discont=true -> continuous=false!