Integration with vertical shift

[math618]

What happens with integration if a function is shifted up/down? As in, they give you an arbitrary function, graphed but not defined, and say int(f(x),0,4) = 4 and ask for int(f(x)+1,0,4). This one has three loops, one +, two -, if that makes a difference. I just guessed at about the amount of area they would lose/gain as they moved up.

[feross]

I haven't taken any sort of Calc for over a year, but here's my two cents.

Wouldn't you just add ((height of vertical shift) * (width of integration)) to the first function? So, in this case, add (1 * 4) = 4 to the arbitrary function, giving you 8 as your final answer.

I don't know if this makes sense or is correct -- take it for what it is.

[math618]

I guess I didn't get around to updating this ... I asked my teacher, and it was really simple:
int(f(x) + 1) = int(f(x)) + int(1)
So yeah

I tried your way at first, but because the curve was both above and below the x-axis, it didn't change consistently.