\(\int\limits_a^b {f\left( x \right)dx}  + \int\limits_b^c {f\left( x \right)dx}  = \int\limits_a^c {f\left( x \right)dx} \)                        

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

\(\int\limits_a^b {f\left( {k.x} \right)dx}  = k\int\limits_a^b {f\left( x \right)dx} \)                         

\(\int\limits_a^b {k.f\left( x \right)dx}  = k.\int\limits_a^b {f\left( x \right)dx} \)