Solve:
1. `int_0^3(ax^2+bx+c)dx`
2. `int_-1^1e^xdx`
3. `int_(-pi//2)^(pi//2) cosx dx`
4. `int_0^10sec^2(3x+6)dx`

Explanation

1.
`I=int_0^3(ax^2+bx+c)dx`
`=((ax^3)/(3)+(bx^2)/(2)+cx)|_0^3`
`=(a(3)^3)/(3)+(b(3)^2)/(2)+c(3)-0`
`=9a+9/2b+3c[:'int_a^bf(x)dx=I(x)|_a^b=I(b)-I(a)]`
2. `I=int_-1^1e^xdx=e^x|_-1^1=e^1-e^-1=e-1/e`
`[because int_a^bf(x)dx=I(x)|_a^b=I(b)-I(a)]`
3. `I=int_(-pi//2)^(pi//2)cosxdx`
`=sinx|_(-pi//2)^(pi//2)`
`=sinpi/2-sin(-pi/2)`
`=1+1=2[ because int_a^bf(x)dx=I(x)|_a^b=I(b)-I(a)]`
4. `I=int_0^10sec^2(3x+6)dx`
`=(tan(3x+6))/(3)|_0^10=1/3[tan(36^(@))-tan(6^(@))]`
`[:'int_a^bf(x)dx=I(x)|_a^b=I(b)-I(a)]`