Evaluate the definite integral.

S4 (-3x+4) dx
1

integral from 1 to 4 of (-3x+4) dx ?

that is the sum of two integrals
-3 x dx and 4 dx

the first one is - (3/2) x^2 at 4 - at 1
= -(3/2)(16 - 1)
= -(3/2) 15 = -45/2

the second one is 4 (4-1) = 12
so I get
-45/2 + 24/2 = -21/2