We know that
[tex]\displaystyle \int_1^4 f(x) \, dx = 8[/tex]
[tex]\displaystyle \int_1^{10} f(x) \, dx = 17[/tex]
By linearity of the definite integral,
[tex]\displaystyle \int_4^{10} 2f(x) - 3 \, dx = 2 \int_4^{10} f(x) \, dx - 3 \int_4^{10} dx[/tex]
Presumably, you're aware that
[tex]\displaystyle \int_a^b dx = b - a[/tex]
for any two numbers a and b, so the last integral is simply 6.
From the known integrals, we also know
[tex]\displaystyle \int_1^{10} f(x) \, dx = \int_1^4 f(x) \, dx + \int_4^{10} f(x) \, dx[/tex]
[tex]\displaystyle 17 = 8 + \int_4^{10} f(x) \, dx[/tex]
[tex]\displaystyle \int_4^{10} f(x) \, dx = 9[/tex]
so
[tex]\displaystyle \int_4^{10} 2f(x) - 3 \, dx = 2\times9- 3\times6 = \boxed{0}[/tex]
