Write equations for the two lines in function notation y = f(x) if they are not already so written. For example, a line that passes through the point (0, 4) and has a slope of 1 is the function y = x + 4.
Label the x values of the boundaries of the region whose area you wish to find "a" and "b" for the left and right boundaries, respectively.
Label the x-value between a and b where the two lines intersect k (skip this step if the two lines do not intersect). For example, if you are finding the area between the two lines y = x + 4 and y = -x + 6, from x = 0 to x = 10, you would label the value x = 1 as k because the two lines intersect when x = 1.
Identify the upper and lower boundary line in the regions a to k and k to b. For each region, make the integrand the difference of the upper and lower boundary line equations. In the above example, the integrand for the region x = 0 to x = 1 is (-x + 6) - (x + 4) and the integrand for the region x = 1 to x = 10 is (x + 4) - (-x + 6).
Calculate the integral for each region using the boundaries of the region as the endpoints of each integral. In the above example, there are two integrals: the integral from 0 to 1 of "(-x + 6) - (x + 4)" and the integral from 1 to 10 of "(x + 4) - (-x +6)."
Add the values of the integrals to find the total area between the two lines.