Geometric Interpretation of Def.Int as Limit of Sum

Q. Let $a,b,c$ be non – zero real numbers such that
${\int }_0^1(1+co{s}^{8}x)(a{x}^2+bx+c)dx={\int }_0^2(1+co{s}^{8}x)(a{x}^2+bx+c)dx.$
Then the quadratic equation $a{x}^2+bx+c=0$ has

1. No root in (0, 2)
2. At least one root in (0, 2)
3. A double root in (0, 2)
4. Two imaginary roots

Q. If $\left[x\right]$ denotes the greater integer less than or equal to x, then the value of ${\int }_1^5[|x-3|]$dx is

1. 1
2. 2
3. 4
4. 8

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