$x^4-2x^2=x^2(x^2-2)\leq0$ when $|x|\leq\sqrt{2}$ and $\geq0$ outside.

To minimise the integral (make it most negative), integrate over the region where the integrand is most negative — i.e., $[-\sqrt{2},\sqrt{2}]$ where the function is $\leq0$.

Any sub-interval of $[-\sqrt{2},\sqrt{2}]$ gives a more negative (or equal) value, and the widest such interval $[-\sqrt{2},\sqrt{2}]$ gives the minimum.

$(a,b)=(-\sqrt{2},\sqrt{2})$

The textbook makes a striking claim about the dominance of non-verbal communication: “As a matter of fact about 90 per cent communication among human beings takes place through their senses and the rest by the use of words as languages.” This statistic reflects the crucial role played by:

• Body language: Facial expressions, posture, gestures, eye contact
• Proxemics: The use of physical space in communication
• Paralanguage: Tone of voice, volume, pitch, rate of speech
• Signs and symbols: Traffic lights, red cross, victory signs — universally understood across language barriers

Despite this, most of recorded human history and civilisation is preserved and transmitted through verbal communication (the remaining 10%). The mass communication industry overwhelmingly relies on verbal communication (print, broadcasting), yet the impact of non-verbal cues — the authority of a leader's voice, the emotion in a photograph — often surpasses the verbal message itself.