Chanceling two definite integrals, that are same, but with different limits I have some stupid question. I am doing some assingment, and I have reached so far: $$ \int_{T/4}^0 \frac{4t}{T}~dt-\int_{T/4}^{T/2} \frac{4t}{T}~dt\\\ $$ I see that this two integrals are the same. Is it possible that I just chancel them out. Thanks

$$ \int_{T/4}^0 - \int_{T/4}^{T/2} \quad = \quad \int_{T/4}^0 + \int^{T/4}_{T/2} \quad = \quad \int_{T/2}^0 $$

In general, $$ \int_a^b+\int_b^c=\int_a^c. $$