`a)`
`f (x) = (2x^4 - 5x^3 + 1)/(x^2)`
`-> F (x) = int f(x)dx`
`-> F (x) = int (2x^4 - 5x^3 + 1)/(x^2)dx`
`-> F (x) = int (2x^2 - 5x + 1/(x^2))dx`
`-> F (x) = (2x^3)/(2 + 1) - (5x^2)/(1 + 1) + (x^{-1})/(-2 + 1) + C`
`-> F (x) = 2/(3)x^3 - 5/(2)x^2 - 1/(x) + C`
`text{Theo giả thuyết}`
`-> F (1) = -3`
`-> 2/(3) - 5/2 - 1 + C= -3`
`-> C = -1/6`
`-> F (x) = 2/(3)x^3 - 5/(2)x^2 - 1/(x) - 1/6`
`b)`
`f (x) = cos^2 x`
`-> F (x) = int cos^2 xdx`
`-> F (x) = int (1 + cos 2x)/(2)dx`
`-> F (x) = int (1/2 + (cos 2x)/(2))dx`
`-> F (x) = 1/(2)x + 1/(2).(1)/(2)sin 2x + C`
`-> F (x) = 1/2(x + sin 2x) + C`
`text{Theo giả thuyết}`
`-> F (\pi)/4 = pi`
`-> 1/(2).[(\pi)/4 + sin ((\pi)/2)] + C = pi`
`-> (\pi)/8 + 1/(4) + C = pi`
`-> C = (7\pi)/8 - 1/4`
`-> F (x) = 1/2(x + sin 2x) + (7\pi)/8 - 1/4`
