The Expand command expands integrals involved in v: ${\int }_a^b\left(sf\left(x\right)+tg\left(x\right)\right)\ⅆx=s\left({\int }_a^{b}f\left(x\right)\ⅆx\right)+t\left({\int }_a^{b}g\left(x\right)\ⅆx\right)$.

$\mathrm{with}\left(\mathrm{IntegrationTools}\right)\:$

$v≔\mathrm{Int}\left(sf\left(x\right)+tg\left(x\right)\,x=a..b\right)$

$v≔{\int }_a^b\left(sf\left(x\right)+tg\left(x\right)\right)\ⅆx$

$\mathrm{Expand}\left(v\right)$

$s\left({\int }_a^{b}f\left(x\right)\ⅆx\right)+t\left({\int }_a^{b}g\left(x\right)\ⅆx\right)$