Question:

<div>Let $f(x) = \int_{0}^{x^2} \frac{t^2 - 5t + 4}{2 + e^t} \, dt$<br/>$f'(x) = \frac{(x^2)^2 - 5(x^2) + 4}{2 + e^{x^2}} \cdot 2x - 0 = \frac{(x^4 - 5x^2 + 4) \cdot 2x}{2 + e^{x^2}} = \frac{(x-1)(x+1)(x-2)(x+2)2x}{2 + e^{x^2}}$<br/>From the wavy curve (graph of $f'(x)$), it is clear that $f'(x)$ changes its sign at $x = \pm 2, \pm 1, 0$ and hence the points of maxima are $-1, 1$ and of the minima are $-2, 0, 2$.</div>