The upper function is 2 minus x, and from that we're going to subtract, from that we're going to subtract the lower function, which is x squared over 4 minus 1. x squared over 4 minus 1. And now we just have to evaluate. So let's first simplify this right over here. This is equal to the definite integral from 0 to 1 of square root of x minus x squared over 4 plus 1 dx, I'm going to write it all in one color now, plus the definite integral from 1 to 2 of 2 minus x minus x squared over 4, then subtracting a negative 1 is a positive 3, or a positive 1, we could just add it to this 2, and so this 2 just becomes a 3. I said 2 minus negative 1 is 3 dx, and now we just have to take the antiderivative and evaluate it at 1 and 0. So the antiderivative of this is, well, this is x to the 1 half, increment it by 1, increment the power by 1, you get x to the 3 halves, and then multiply by the reciprocal of the new exponent, so it's 2 thirds x to the 3 halves, minus the antiderivative of x squared over 4 is x to the 3rd divided by 3 divided by 4, so divided by 12, plus x, that's the antiderivative of 1, we're going to evaluate it at 1 and 0, and then here the antiderivative is going to be 3x minus x squared over 2, minus x to the 3rd over 12, once again evaluated at, well not once again, now we're going to evaluate at 2 and 1. So over here you evaluate all of this stuff at 1, you get 2 thirds minus 1 12th plus 1, and then from that you subtract this evaluated at 0, but this is just all 0, so you get nothing, so this is what the yellow stuff simplified to, and then this purple stuff, or this magenta stuff, or mauve, or whatever color this is, first you evaluate it at 2, you get 6 minus, let's see, 2 squared over 2 is 2, minus 8 over 12, and then from that you're going to subtract this evaluated at 1, so it's going to be 3 times 1, minus 1 half, minus 1 over 12, and now what we're essentially left with is adding a bunch of fractions, so let's see if we can do that, it looks like 12 would be the most obvious common denominator, so here you have 8 over 12 minus 1 over 12, plus 12 over 12, so this simplifies to, this is 19 over 12, the part that we have in yellow, then this business, let me do it in this color, so 6 minus 2, this is just going to be 4, so we can write this as 48 over 12, that's 4, minus 8 over 12, and then we're going to have to subtract a 3, which is 36 over 12, then we're going to add 1 half, which is just plus 6 over 12, and then we're going to add a 1 twelfth, so this is all going to simplify to, let's see, 48 minus 8 is 40, minus 36 is 4, plus 6 is 10, plus 1 is 11, so this becomes plus 11 over 12, let me make sure I did that right, 48 minus 8 is 40, minus 36 is 4, 10, 11, so that looks right, and then we're ready to add these two, 19 plus 11 is equal to 30 over 12, or if we want to simplify this a little bit, we can divide the numerator and the denominator by 6, this is equal to 5 halves, or 2 and a half, and we're done, we figured out the area of this entire region, it is 2 and a half.