The region defined is symmetric about the y-axis. We find the area for x≥0 and double the result. The boundary functions are y=2x+1 and y=x2+1 within 0≤x≤3. They intersect at x=0 and x=2. The total area is calculated by integrating the lower function in each interval: Ahalf=
2
∫
0
(x2+1)‌dx+
3
∫
2
(2x+1)‌dx Evaluate the integrals: [‌
x3
3
+x]02=‌
14
3
[x2+x]23=6 Sum the half-area components: A‌half ‌=‌
