$$ \int_{1}^4|x|dx $$
I know how to take the integral of a more complex function (like f(x)= |x+2|) but I don't understand what to do if it's just the absolute value of x. If the lowest number is 1 does that mean I only have to do $$ \int_{1}^4xdx $$
or am I not understanding this correctly?
Yes, you are correct; the two integrals are the same since |x| = x on the interval from 1 to 4. If you ever need to take the integral of some strange function, it's worth remembering that integrating something is simply finding the limit of the sum of increasingly thinner rectangles approximating the area under the function. The fact that this happens to correspond to anti-derivatives is a higher level result, but there are plenty of functions that can be integrated in this more fundamental way that do not have derivatives.