Question: The use of Heaviside

I have the following integration:

Int(c-sqrt(a+b*(v*x+u)^2), x = -(b*u+sqrt(b*c^2-a*b))/(b*v) .. (-b*u+sqrt(b*c^2-a*b))/(b*v));

This integration is equivalent to the following integration (between dashed lines):

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NumericEventHandler(invalid_operation = `Heaviside/EventHandler`(value_at_zero = 1)):

Heaviside(0)

Heaviside(x) = convert(Heaviside(x), piecewise)

Int(Heaviside(x+(b*u+sqrt(b*c^2-a*b))/(b*v))*(c-sqrt(a+b*(v*x+u)^2)), x = -infinity .. (-b*u+sqrt(b*c^2-a*b))/(b*v));

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In this form the function, which is to be integrated, is taken as equal to zero for x < -(b*u+sqrt(b*c^2-a*b))/(b*v).

Now I want to write a form such that the function is also taken as equal to zero for x > (-b*u+sqrt(b*c^2-a*b))/(b*v).

How should I do this? Can this also be done with Heaviside?