Nếu \(\int\limits_a^d {f\left( x \right)dx} = 5,\int\limits_b^d {f\left( x \right)dx} = 2\) với \(a < d < b\) thì \(\int\limits_a^b {f\left( x \right)dx} \) có giá trị bằng:

\(\int\limits_a^b {f\left( x \right)dx}  = \int\limits_a^d {f\left( x \right)dx}  + \int\limits_d^b {f\left( x \right)dx}  = \int\limits_a^d {f\left( x \right)dx}  - \int\limits_b^d {f\left( x \right)dx}  = 5 - 2 = 3\).