we are given
[tex]\int _2^6f\left(x\right)dx=12\:[/tex]
[tex]\int _2^6g\left(x\right)dx=24\:[/tex]
we can find
[tex]\int _2^6(6f(x)-2g(x) +5)dx\:[/tex]
we can distribute it
[tex]=6\int _2^6 f(x)dx-2\int _2^6 g(x)dx +\int _2^6 5dx[/tex]
we can plug values
and we get
[tex]=6*12-2*24 +\int _2^6 5dx[/tex]
[tex]\int _2^6\:5dx[/tex]
[tex]\int \:5dx[/tex]
[tex]=5x[/tex]
now, we can plug bounds
and we get
[tex]=30-10[/tex]
[tex]=20[/tex]
[tex]=6*12-2*24 +20[/tex]
[tex]=44[/tex]................Answer