We use optical integral field spectroscopy ( IFS ) of nearby supernova ( SN ) host galaxies ( 0.005 < z < 0.03 ) provided by the Calar Alto Legacy Integral Field Area ( CALIFA ) Survey with the goal of finding correlations in the environmental parameters at the location of different SN types . In this first study of a series we focus on the properties related with star formation ( SF ) . We recover the sequence in association of different SN types to the star-forming regions by using several indicators of the ongoing and recent SF related to both the ionized gas and the stellar populations . While the total ongoing SF is on average the same for the three SN types , SNe Ibc/IIb tend to occur closer to star-forming regions and in higher SF density locations than SNe II and SNe Ia ; the latter shows the weakest correlation . SNe Ia host galaxies have masses that on average are \sim 0.3-0.8 dex higher than those of the core collapse ( CC ) SNe hosts because the SNe Ia hosts contain a larger fraction of old stellar populations . Using the recent SN Ia delay-time distribution and the SFHs of the galaxies , we show that the SN Ia hosts in our sample are expected to produce twice as many SNe Ia as the CC SN hosts . Since both types occur in hosts with a similar SF rate and hence similar CC SN rate , this can explain the mass difference between the SN Ia and CC SN hosts , and reinforces the finding that at least part of the SNe Ia originate from very old progenitors . By comparing the mean SFH of the eight least massive galaxies with that of the massive SF SN Ia hosts , we find that the low-mass galaxies formed their stars during a longer time ( 0.65 % , 24.46 % , and 74.89 % in the intervals 0–0.42 Gyr , 0.42–2.4 Gyr , and > 2.4 Gyr , respectively ) than the massive SN Ia hosts ( 0.04 % , 2.01 % , and 97.95 % in these intervals ) . We estimate that the low-mass galaxies produce ten times fewer SNe Ia and three times fewer CC SNe than the high-mass group . Therefore the ratio between the number of CC SNe and SNe Ia is expected to increase with decreasing galaxy mass . CC SNe tend to explode at positions with younger stellar populations than the galaxy average , but the galaxy properties at SNe Ia locations are one average the same as the global galaxy properties .