calculus - Definition of Unsigned Definite Integral

In Terence Tao's paper Differential Forms and Integration, he mentions that there are $3$ distinct notions of integration when discussing functions $f: \Bbb R \to \Bbb R$

• Indefinite Integrals: $\int f(x)\ dx$


• Unsigned Definite Integrals: $\int_{[a,b]} f(x)\ dx$


• Signed Definite Integrals: $\int_a^b f(x)\ dx$

I know well the definitions of indefinite integral -- $\int f(x)\ dx = F(x) \iff F'(x) = f(x)$ -- and the signed definite integral -- via the Darboux or Riemann sum definitions. But I've never heard of an unsigned definite integral and I can't find a rigorous definition of it.

What is the definition of the unsigned definite integral?