# definite integral question

The graph of $y= \frac{3}{4}- x- x^2$ is a parabola opening downward. Also $\frac{3}{4}- x- x^2= \frac{-1}{4}(4x^2+ 4x- 3)= \frac{-1}{4}(2x- 3)(2x+ 1)= 0$ when x= 3/2 or -1/2. If a and b are both between -1/2 and 3/2, then the integral from a to b is less than the integral from -1/2 to 3/2. If either or both is outside that interval, you will be subtracting from that.