Geometric Interpretation of Def.Int as Limit of Sum

Q. If $f\left(x\right)$ is a continuous function defined on $[a,b]$ such that $f\left(x\right)\ge 0$ $x\in [a,b]$ then the area under the curve as the limit of a sum can be given as
$(b-a)\underset{n\to \infty }{lim}\frac{1}{n}\left[f\right(a)+f(a+h)...f(a+(n-1)h\left)\right]$
Where $h=\frac{b-a}{n}$ and $h\to 0$ as $n\to \infty$

1. True
2. False

Q. Let $I=\underset{a}{\overset{b}{\int }}(x^4-2x^2)dx$. If $I$ is minimum then the ordered pair $(a,b)$ is :

1. $(0,\sqrt{2})$
2. $(-\sqrt{2},0)$
3. $(-\sqrt{2},\sqrt{2})$
4. $(\sqrt{2},-\sqrt{2})$

Q. If $f:[1,\infty )\to B$ defined by the function $f\left(x\right)=x^2-2x+6$ is a surjection, then $B$ is equal to

1. $[5,\infty )$
2. $[6,\infty )$
3. $[2,\infty )$
4. $[1,\infty )$