\(\int\limits_a^b {\left| {f\left( x \right) - g\left( x \right)} \right|dx}  = \int\limits_a^b {f\left( x \right)dx}  - \int\limits_a^b {g\left( x \right)dx} \)

\(\int\limits_a^b {\left[ {f\left( x \right) - g\left( x \right)} \right]dx}  = \int\limits_a^b {f\left( x \right)dx}  - \int\limits_a^b {g\left( x \right)dx} \)

\(\left| {\int\limits_a^b {\left[ {f\left( x \right) - g\left( x \right)} \right]} } \right|dx = \int\limits_a^b {f\left( x \right)dx}  - \int\limits_a^b {g\left( x \right)dx} \)

\(\int\limits_a^b {\left[ {f\left( x \right) - g\left( x \right)} \right]dx}  = \left| {\int\limits_a^b {f\left( x \right)dx}  - \int\limits_a^b {g\left( x \right)dx} } \right|\)