Verified Answer :

eternal3fear

anti derivative of 4 is 4x
anti derivative of -x is -1/2 x^2

so  y = 4x - (1/2)x^2 + C
(can't forget constants when doing anti derivatives xD)

is this what you need?

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Anti-derivative of a Constant [just a number] becomes  (constant)x
for example  integral of 5 = 5x + C

Then there is a Power Rule for integrals
integral of (x)^n = 1/(n+1) (x)^(n+1) + C
for example: integral of  x^2 = 1/(2+1) (x)^(2+1) + C = (1/3)*x^3 + C

We have dy/dx = (4-x) dx which is a first order linear ODE

dy = (4-x) dx. Now integrating both sides we get:

y = 4x - 1/2 x^2 + C

which is the answer. Note we only wrote +c once since we can combine arbitrary constants under addition and subtraction with each other.

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